Factor Analysis for Detector Dog C-BARQ for Combined Phase 1 and Phase 2 Data

Version 2.0 of Combined Factor Analysis (No Chasing Data) Using Items with Communality greater than or equal to0.40 from analysis 1.0

lizhare@gmail.com

1 Context

1.1 Overall Factor Analysis Steps

1. Are the data suitable for factor analysis?
   • Bartlett’s Sphericity Test Tests whether correlations are different than zero across all the data. If they are close to zero, there owuld be no common factors to find
   • Kaiser-Meyer-Olkin Criterion Test sampling adequacy, measures the degree to wich each variable predicts all other variables in the data set.
2. Imputation of Missing Variables
   • Generate categorical values for missing data using Multiple Correspondence Analysis/Missing Fuzzy Average Method
3. Calculate between-item Correlations
   • the polychoric (for orderd categorical variables) and regular Pearson correlation are calculated for later use in factor analysis and for checking other aspects of the factor analysis. The polychoric correlation is the input to the actual factor analysis.
4. Estimate Number of Factors
   • Parallel analysis
     
   • Minimim Average Partial (MAP)
5. Run factor analysis for a range of possible number of factors
   • produces
     • measures of model fit
       
     • communalities (how much each item covaries with the other items)
       
     • loadings (correlation between item and factor(s))
6. Evaluate Reliability of Model..
   • alpha
     
   • omega
7. Select best model (number of factors) given model fit statistics and judgement based on understanding of behavior.

1.2 Context Text Description

All data were used in the factorAnalysis1.1.html document you already received.

A series of factoro analyses were run on all items in the file factorAnalysis1.1.html. THe literature suggests doing this so you can compare both statistical measures of how well it fits, and also how logical the grouping of factors is according to knowledge of the subject.

This set of analyses showed that some items had really low communalities, meaning that they didn’t covary much with any of the other items. This means they will not be robust parts of any factor, and they recommend that you remove these from the analysis.

Models with different numbers of factors had different numbers of items with communalities less than 0.4. So a new data set was made for each number of factors, with only the items with communalities of 0.4 or larger.

Because each number of factors require a different data set (different numbers of items), all the steps had to be rerun sstarting with imputation. Those are the models included in this document.

2 Factor Analyses

Testing analyses from 11 - 18 factors.

2.1 11 Factors

2.1.1 Imputation of Missing Items (11 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.1.2 11-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.1.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum11, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1906 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 2211 DF, p = NaN.

2.1.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.3 11-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.1.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF11, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1904 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 2211 DF, p = NaN.

2.1.3.2 11-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.4 Between-Item Correlations

2.1.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.889.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.887.

2.1.5 Estimating Number of Factors

2.1.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF11, n.obs = nrow(imputedNumericDF11), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 14.

2.1.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

Number of Factors	MAP value
1	0.0251
2	0.0208
3	0.0163
4	0.0147
5	0.0142
6	0.0133
7	0.0126
8	0.0121
9	0.0118
10	0.0117
11	0.0115
12	0.0113
13	0.0113
14	0.0117
15	0.0117
16	0.0120
17	0.0121
18	0.0126

2.1.6 Factor Analysis for 11 Factors

2.1.6.1 11 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1904 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.742761^{4}
  
• degrees of freedom: 1529
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.1162773. Should be > 0.9; need reference)

2.1.6.2 11 Factor Model Communalities

	fanal11.communality
TRAIN01	0.44
TRAIN02	0.24
TRAIN04	0.61
TRAIN05	0.32
TRAIN06	0.25
TRAIN07	0.60
TRAIN08	0.61
AGG09	0.76
AGG10	0.63
AGG11	0.76
AGG12	0.79
AGG13	0.95
AGG14	0.45
AGG15	0.76
AGG16	0.73
AGG17	0.55
AGG18	0.72
AGG19	0.59
AGG20	0.47
FEAR21	0.81
FEAR22	0.32
FEAR23	0.78
FEAR24	0.84
FEAR25	0.46
FEAR27	0.67
FEAR28	0.64
FEAR29	0.13
FEAR31	0.59
SEPR32	0.69
SEPR33	0.53
SEPR34	0.73
EXCITE35	0.48
EXCITE36	0.63
EXCITE37	0.58
EXCITE38	0.62
ATT39	0.30
ATT40	0.28
ATT41	0.32
ATT42	0.35
PLAY43	0.55
PLAY44	0.79
PLAY45	0.74
PLAY46	0.71
IMP47	0.46
IMP48	0.41
IMP49	0.39
MISC50	0.32
MISC51	0.37
MISC52	0.23
MISC54	0.58
MISC55	0.70
MISC56	0.53
MISC57	0.33
MISC58	0.23
MISC59	0.54
MISC60	0.38
MISC61	0.50
MISC62	0.48
MISC63	0.37
MISC64	0.54
MISC65	0.60
MISC66	0.69
MISC67	0.62
MISC68	0.20
MISC69	0.22
MISC70	0.33
MISC71	0.28

2.1.6.3 How many communalities < 0.40?

There are 21 items with communality < 0.40.

	fanal11.communality	item
TRAIN02	0.24	TRAIN02
TRAIN05	0.32	TRAIN05
TRAIN06	0.25	TRAIN06
FEAR22	0.32	FEAR22
FEAR29	0.13	FEAR29
ATT39	0.30	ATT39
ATT40	0.28	ATT40
ATT41	0.32	ATT41
ATT42	0.35	ATT42
IMP49	0.39	IMP49
MISC50	0.32	MISC50
MISC51	0.37	MISC51
MISC52	0.23	MISC52
MISC57	0.33	MISC57
MISC58	0.23	MISC58
MISC60	0.38	MISC60
MISC63	0.37	MISC63
MISC68	0.20	MISC68
MISC69	0.22	MISC69
MISC70	0.33	MISC70
MISC71	0.28	MISC71

2.1.6.4 11 Factor Model Loadings

	PA2	PA10	PA1	PA5	PA11	PA6	PA8	PA3	PA4	PA7	PA9
TRAIN01	-0.14	-0.12	0.17	-0.02	-0.09	0.06	0.04	0.05	0.54	-0.02	-0.01
TRAIN02	-0.04	0.06	0.14	-0.02	0.00	0.03	0.01	-0.03	0.40	0.09	-0.05
TRAIN04	-0.04	0.05	0.30	0.01	-0.02	0.05	-0.04	-0.04	0.63	0.02	-0.08
TRAIN05	0.04	-0.15	0.12	0.14	-0.06	0.00	-0.02	0.13	0.43	0.07	0.02
TRAIN06	-0.09	0.02	0.21	-0.04	0.10	0.07	0.06	-0.12	0.29	-0.03	-0.13
TRAIN07	-0.13	0.02	0.60	-0.02	-0.03	0.05	0.03	-0.07	0.27	0.00	-0.06
TRAIN08	-0.74	0.01	0.08	0.01	0.06	0.01	-0.05	-0.03	0.06	0.05	0.03
AGG09	0.05	0.29	0.07	0.06	0.03	-0.06	0.08	0.71	0.03	-0.05	0.04
AGG10	0.03	0.05	-0.04	0.06	-0.03	0.06	0.18	0.68	-0.04	0.01	-0.01
AGG11	-0.09	-0.02	-0.13	0.81	0.00	0.12	0.04	0.01	0.09	-0.12	0.07
AGG12	-0.04	0.08	0.06	0.88	0.01	-0.03	-0.01	-0.04	-0.07	0.04	-0.03
AGG13	-0.01	0.03	0.02	0.95	0.01	-0.10	-0.02	0.07	0.03	0.05	0.01
AGG14	-0.09	0.05	-0.03	-0.07	0.05	0.08	0.16	0.59	-0.01	0.06	0.09
AGG15	-0.02	0.26	0.00	0.13	0.01	-0.03	0.06	0.70	0.01	-0.02	-0.04
AGG16	0.00	-0.04	0.09	0.02	0.02	-0.03	0.75	0.25	-0.01	0.00	-0.05
AGG17	0.10	0.08	-0.01	0.17	0.21	0.22	0.08	0.36	0.08	0.11	-0.34
AGG18	0.06	-0.08	0.05	0.03	-0.03	0.02	0.75	0.27	-0.02	-0.03	0.02
AGG19	0.15	-0.11	0.06	0.30	0.02	0.13	0.57	0.10	-0.06	0.10	-0.13
AGG20	0.02	-0.13	0.01	0.48	0.02	0.12	0.41	-0.07	-0.07	0.02	-0.04
FEAR21	0.01	0.83	0.03	0.07	0.02	0.06	-0.04	0.13	0.00	0.01	-0.04
FEAR22	-0.04	0.25	0.23	0.06	0.24	0.08	0.05	-0.21	-0.10	0.05	-0.04
FEAR23	0.00	0.79	0.01	0.00	0.06	0.05	0.01	0.18	-0.01	-0.02	0.02
FEAR24	-0.08	0.83	0.03	0.06	-0.01	0.00	0.00	0.15	-0.05	0.03	0.00
FEAR25	0.02	0.28	0.21	0.13	0.35	0.03	0.02	-0.08	0.05	0.02	0.06
FEAR27	-0.04	0.45	-0.10	-0.03	0.10	-0.04	0.59	-0.18	0.11	-0.03	0.10
FEAR28	0.06	0.49	0.20	0.06	0.38	0.06	-0.02	-0.09	-0.03	0.06	-0.09
FEAR29	-0.07	0.12	0.05	0.11	0.08	0.08	0.11	-0.04	0.08	0.08	-0.02
FEAR31	-0.07	0.42	-0.04	-0.04	0.12	-0.02	0.52	-0.29	0.11	-0.01	0.09
SEPR32	0.00	0.12	0.06	-0.02	-0.07	0.81	0.05	-0.04	-0.10	0.08	-0.06
SEPR33	-0.01	-0.01	0.08	0.05	-0.01	0.69	0.00	-0.08	-0.02	0.03	0.04
SEPR34	-0.03	-0.05	-0.07	-0.06	0.11	0.82	-0.04	0.06	0.12	-0.03	0.04
EXCITE35	-0.11	0.09	0.04	-0.11	-0.10	0.16	0.01	0.02	-0.05	0.64	0.06
EXCITE36	0.20	-0.01	0.05	0.00	0.02	-0.05	-0.08	0.03	-0.01	0.73	-0.04
EXCITE37	-0.07	-0.01	-0.05	0.02	-0.02	0.03	0.03	-0.01	0.04	0.77	-0.02
EXCITE38	0.03	-0.02	-0.14	0.05	0.09	-0.04	0.01	-0.05	0.06	0.76	0.00
ATT39	-0.06	0.09	0.14	-0.13	-0.11	0.08	0.03	0.09	-0.38	0.23	0.22
ATT40	-0.20	0.07	0.29	-0.03	0.08	0.13	0.03	0.05	-0.15	0.11	0.14
ATT41	-0.06	-0.02	0.13	0.08	-0.02	0.11	0.02	-0.07	-0.21	0.12	0.45
ATT42	-0.12	-0.02	0.09	0.02	0.07	0.13	0.10	-0.01	-0.04	0.16	0.43
PLAY43	0.52	-0.25	-0.02	-0.04	0.05	-0.09	0.00	-0.30	-0.02	0.06	0.12
PLAY44	0.88	0.00	0.03	-0.01	-0.01	0.00	0.08	-0.05	0.02	0.06	-0.02
PLAY45	0.82	0.06	-0.01	-0.09	-0.03	-0.06	0.02	0.00	-0.05	0.01	0.06
PLAY46	0.77	-0.04	-0.14	-0.02	0.03	0.05	-0.06	0.09	0.07	0.04	-0.08
IMP47	0.21	0.09	-0.06	0.02	-0.01	0.04	0.05	0.00	0.43	0.17	0.29
IMP48	0.15	0.04	0.04	0.20	0.00	0.05	0.05	-0.05	0.28	0.13	0.32
IMP49	0.00	0.05	0.05	0.20	-0.02	-0.06	0.01	0.00	0.44	0.16	0.16
MISC50	0.04	0.00	-0.02	0.21	0.09	0.24	-0.06	0.02	0.20	0.08	0.21
MISC51	-0.13	-0.16	-0.01	0.02	0.02	0.28	0.01	0.11	0.35	0.05	0.17
MISC52	-0.32	-0.04	0.00	0.06	0.05	-0.07	0.05	0.00	0.05	0.11	0.34
MISC54	-0.11	0.02	0.16	-0.01	0.67	-0.02	0.02	-0.04	0.00	0.08	-0.02
MISC55	0.02	-0.03	-0.04	-0.06	0.87	0.02	0.01	0.04	-0.07	0.00	0.00
MISC56	-0.03	-0.03	0.03	0.11	0.71	-0.03	-0.04	0.01	0.01	-0.04	0.03
MISC57	0.06	-0.06	0.10	0.14	-0.05	0.16	-0.01	-0.05	0.24	0.10	0.26
MISC58	0.13	-0.03	0.05	0.33	0.01	0.26	-0.04	0.00	0.04	-0.12	0.11
MISC59	0.27	0.05	0.14	0.10	-0.02	0.37	-0.08	-0.04	0.13	-0.01	0.37
MISC60	0.30	0.02	0.07	-0.04	-0.03	0.06	-0.14	0.01	-0.01	0.14	0.41
MISC61	0.42	0.01	0.04	-0.02	-0.12	0.17	-0.13	0.11	-0.06	0.16	0.30
MISC62	0.00	-0.03	0.40	-0.04	-0.01	-0.06	0.41	0.04	0.09	0.04	0.22
MISC63	-0.01	-0.02	0.35	0.04	0.11	-0.14	0.08	0.05	0.09	0.14	0.31
MISC64	-0.07	-0.14	0.66	0.00	0.06	0.05	0.02	0.07	0.08	-0.04	0.00
MISC65	-0.09	-0.12	0.62	-0.03	0.05	0.05	0.14	0.04	0.15	-0.04	0.09
MISC66	-0.05	0.21	0.63	-0.01	0.18	0.05	-0.06	0.00	0.07	-0.06	0.02
MISC67	-0.07	0.20	0.62	0.07	0.11	0.07	-0.01	-0.03	-0.06	-0.06	0.05
MISC68	0.02	-0.12	-0.09	0.11	0.31	0.07	0.00	0.12	0.19	0.05	0.08
MISC69	-0.06	-0.05	-0.07	-0.01	0.33	0.10	0.03	0.11	0.14	0.03	0.20
MISC70	0.02	-0.06	-0.05	0.07	0.08	0.14	0.08	0.19	0.08	0.00	0.43
MISC71	-0.03	-0.04	0.08	-0.05	0.26	0.10	-0.07	0.08	0.05	-0.06	0.38

2.1.6.4.1 11 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
14	PA1	0.29	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
45	PA1	0.35	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
46	PA1	0.66	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
47	PA1	0.62	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
48	PA1	0.63	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
49	PA1	0.62	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
66	PA1	0.60	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
67	PA1	0.08	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
21	PA10	0.83	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
22	PA10	0.25	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
23	PA10	0.79	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24	PA10	0.83	FEAR24	When an unfamiliar person tries to touch or pet the dog
27	PA10	0.49	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
28	PA10	0.12	FEAR29	When having nails trimmed, or feet touched/handled
25	PA11	0.35	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
36	PA11	0.67	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
37	PA11	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
38	PA11	0.71	MISC56	Nervous or frightened when ascending or descending some types of stairs
50	PA11	0.31	MISC68	Chases own tail/hind end
51	PA11	0.33	MISC69	Chases/follows shadows, light spots, etc.
43	PA2	0.42	MISC61	Active, energetic, always on the go
54	PA2	0.52	PLAY43	Eagerly engages in play with new/unfamiliar people
55	PA2	0.88	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56	PA2	0.82	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57	PA2	0.77	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.71	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.68	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.59	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.70	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA3	0.36	AGG17	When stared at directly by you or another familiar person
30	PA4	0.43	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA4	0.44	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
34	PA4	0.35	MISC51	Escapes or would escape from home, yard or kennel given the chance
61	PA4	0.54	TRAIN01	Is hard to recall when off the leash
62	PA4	0.40	TRAIN02	Is slow to obey a ‘sit’ command
63	PA4	0.63	TRAIN04	Has difficulty attending/listening to things you say or do
64	PA4	0.43	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
65	PA4	0.29	TRAIN06	Is slow to learn new tricks or tasks
3	PA5	0.81	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA5	0.88	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA5	0.95	AGG13	When his/her food is taken away by you or another familiar person
12	PA5	0.48	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
40	PA5	0.33	MISC58	Urinates against objects/furnishings indoors
33	PA6	0.24	MISC50	NA
41	PA6	0.37	MISC59	Hyperactive, restless, has trouble settling down
58	PA6	0.81	SEPR32	Restlessness/agitation/pacing when left alone
59	PA6	0.69	SEPR33	Barking or whining when left alone
60	PA6	0.82	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
13	PA7	0.23	ATT39	Displays a strong attachment for you or another familiar person
17	PA7	0.64	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18	PA7	0.73	EXCITE36	Excitable when playing with you or other familiar persons
19	PA7	0.77	EXCITE37	Excitable just before being taken out for a walk
20	PA7	0.76	EXCITE38	Excitable just before being taken out for work or training
8	PA8	0.75	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.75	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.57	AGG19	Towards other familiar dogs
26	PA8	0.59	FEAR27	When approached directly by an unfamiliar dog
29	PA8	0.52	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
44	PA8	0.41	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
15	PA9	0.45	ATT41	Tends to nudge or paw you (or others) for attention
16	PA9	0.43	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31	PA9	0.32	IMP48	Becomes frustrated/impatient in a wide range of situations
35	PA9	0.34	MISC52	Begs persistently for food when people are eating
39	PA9	0.26	MISC57	Pulls excessively hard when on leash
42	PA9	0.41	MISC60	Playful, puppyish, boisterous
52	PA9	0.43	MISC70	Barks persistently when alarmed or excited
53	PA9	0.38	MISC71	Licks people or objects excessively

2.1.7 11 Model Reliability Measures

2.2 12 Factors

2.2.1 Imputation of Missing Items (12 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.2.2 12-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.2.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum12, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1232 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.2.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8457672

2.2.3 12-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.2.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF12, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1232 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.2.3.2 12-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8457672

2.2.4 Between-Item Correlations

2.2.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.9.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.692. The maximum correlation was 0.904.

2.2.5 Estimating Number of Factors

2.2.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF12, n.obs = nrow(imputedNumericDF12), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 12.

2.2.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0326
2	0.0279
3	0.0219
4	0.0203
5	0.0193
6	0.0178
7	0.0174
8	0.0163
9	0.0156
10	0.0149
11	0.0153
12	0.0151
13	0.0157
14	0.0163
15	0.0170
16	0.0176
17	0.0181
18	0.0189

2.2.6 Factor Analysis for 12 Factors

2.2.6.1 12 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1232 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.1891719^{4}
  
• degrees of freedom: 808
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0349984. Should be > 0.9; need reference)

2.2.6.2 12 Factor Model Communalities

	fanal12.communality
TRAIN01	0.47
TRAIN03	0.41
TRAIN04	0.58
TRAIN07	0.63
TRAIN08	0.62
AGG09	0.75
AGG10	0.67
AGG11	0.76
AGG12	0.76
AGG13	1.00
AGG14	0.50
AGG15	0.79
AGG16	0.78
AGG17	0.62
AGG18	0.75
AGG19	0.60
AGG20	0.45
FEAR21	0.82
FEAR23	0.79
FEAR24	0.86
FEAR25	0.43
FEAR26	0.35
FEAR27	0.68
FEAR28	0.65
FEAR30	0.31
FEAR31	0.58
SEPR32	0.69
SEPR33	0.60
SEPR34	0.68
EXCITE35	0.48
EXCITE36	0.61
EXCITE37	0.61
EXCITE38	0.64
PLAY43	0.56
PLAY44	0.81
PLAY45	0.77
PLAY46	0.71
IMP47	0.45
IMP48	0.41
MISC52	0.53
MISC53	0.52
MISC54	0.64
MISC55	0.72
MISC56	0.62
MISC59	0.50
MISC60	0.53
MISC61	0.68
MISC62	0.45
MISC64	0.64
MISC65	0.64
MISC66	0.68
MISC67	0.58
MISC68	0.14

2.2.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

	fanal12.communality	item
FEAR26	0.35	FEAR26
FEAR30	0.31	FEAR30
MISC68	0.14	MISC68

2.2.6.4 12 Factor Model Loadings

	PA1	PA2	PA4	PA12	PA5	PA9	PA6	PA8	PA7	PA3	PA11	PA10
TRAIN01	-0.09	-0.06	-0.02	0.13	0.05	-0.07	0.02	0.01	-0.04	0.60	-0.07	0.06
TRAIN03	-0.01	-0.09	-0.08	-0.04	0.07	0.06	-0.02	0.07	0.09	0.59	0.03	0.04
TRAIN04	0.07	-0.03	0.03	0.26	-0.01	-0.02	-0.06	-0.01	0.02	0.63	-0.02	-0.01
TRAIN07	0.05	-0.11	0.01	0.61	0.01	-0.05	-0.09	0.02	0.01	0.29	-0.02	-0.05
TRAIN08	0.03	-0.70	0.02	0.12	-0.04	0.07	-0.04	0.00	0.04	0.05	-0.03	0.08
AGG09	0.29	0.03	0.06	0.03	0.15	0.06	0.65	-0.07	-0.07	0.07	0.09	-0.04
AGG10	0.01	0.09	0.06	0.01	0.17	-0.04	0.71	0.10	-0.01	-0.08	-0.06	0.07
AGG11	0.00	-0.07	0.81	-0.14	0.07	-0.01	-0.03	0.10	-0.11	0.15	0.01	0.02
AGG12	0.05	-0.09	0.86	0.04	0.00	0.02	-0.02	0.00	0.05	-0.10	0.01	0.00
AGG13	0.03	0.03	0.99	0.07	-0.03	-0.01	0.06	-0.07	0.04	-0.03	0.00	0.04
AGG14	0.03	0.01	-0.08	0.08	0.13	-0.02	0.62	0.11	0.06	-0.07	-0.09	0.14
AGG15	0.27	-0.03	0.12	-0.02	0.10	0.02	0.70	-0.03	-0.02	0.02	0.03	0.01
AGG16	-0.02	-0.06	-0.01	0.02	0.82	0.06	0.18	-0.05	0.00	0.04	0.00	-0.06
AGG17	0.07	0.22	0.21	0.13	0.02	0.09	0.34	0.19	0.15	0.01	-0.40	-0.20
AGG18	-0.06	0.01	0.02	-0.01	0.81	0.00	0.19	0.01	-0.04	0.05	0.02	-0.02
AGG19	-0.08	0.06	0.27	-0.03	0.62	0.04	0.04	0.09	0.12	0.03	-0.03	-0.15
AGG20	-0.11	0.03	0.44	-0.06	0.39	0.03	-0.06	0.11	0.02	0.03	-0.10	0.01
FEAR21	0.86	-0.01	0.07	-0.03	-0.05	0.03	0.11	0.03	0.00	0.03	0.01	-0.04
FEAR23	0.81	-0.03	0.00	0.00	0.01	0.05	0.14	0.05	-0.01	-0.02	0.03	-0.06
FEAR24	0.87	-0.10	0.06	-0.01	-0.01	-0.03	0.11	-0.01	0.04	-0.03	0.01	-0.02
FEAR25	0.32	0.05	0.09	0.18	0.00	0.30	-0.09	0.05	0.04	0.11	-0.07	0.01
FEAR26	0.45	0.09	0.14	0.01	0.03	0.05	-0.01	0.13	0.00	0.03	-0.09	0.12
FEAR27	0.45	0.05	-0.01	0.08	0.51	0.02	-0.21	-0.01	-0.01	-0.11	-0.10	0.22
FEAR28	0.53	0.07	0.03	0.11	-0.06	0.38	-0.10	0.07	0.06	0.05	-0.11	-0.05
FEAR30	0.14	0.11	0.17	0.06	0.05	0.18	-0.08	0.20	-0.01	0.04	-0.17	0.17
FEAR31	0.40	0.04	-0.04	0.11	0.41	0.06	-0.28	0.01	0.00	-0.08	-0.13	0.26
SEPR32	0.10	-0.05	-0.05	0.00	0.03	-0.05	0.00	0.82	0.07	-0.05	0.01	-0.05
SEPR33	-0.04	-0.03	0.05	0.06	-0.02	0.00	-0.06	0.76	-0.02	-0.03	0.07	0.03
SEPR34	-0.06	0.00	-0.04	0.00	-0.05	0.06	0.06	0.81	-0.04	0.07	-0.01	0.03
EXCITE35	0.10	-0.15	-0.11	0.02	0.03	-0.08	0.02	0.14	0.63	-0.01	0.12	0.02
EXCITE36	0.00	0.16	0.03	0.05	-0.07	0.03	0.02	-0.05	0.70	-0.03	0.08	-0.04
EXCITE37	-0.02	-0.08	0.01	-0.01	0.03	-0.03	0.00	0.01	0.80	0.01	0.01	0.02
EXCITE38	-0.02	0.05	0.04	-0.11	0.00	0.06	-0.05	-0.03	0.77	0.05	-0.04	0.04
PLAY43	-0.26	0.50	-0.02	0.03	-0.03	0.01	-0.28	-0.07	0.07	-0.09	0.11	0.07
PLAY44	0.00	0.85	0.00	0.00	0.06	-0.03	-0.05	-0.01	0.05	0.03	0.05	-0.09
PLAY45	0.03	0.83	-0.09	0.01	-0.03	-0.04	0.05	-0.05	0.00	-0.10	0.07	0.05
PLAY46	-0.06	0.77	-0.02	-0.14	-0.08	0.00	0.12	0.03	0.03	0.06	-0.01	-0.05
IMP47	0.08	0.30	0.02	-0.03	0.04	0.01	0.02	0.05	0.12	0.38	0.14	0.29
IMP48	0.03	0.22	0.17	0.05	0.05	0.02	-0.02	0.10	0.11	0.25	0.15	0.29
MISC52	-0.08	-0.13	0.01	0.04	-0.08	0.06	0.17	-0.01	0.07	-0.01	-0.03	0.70
MISC53	-0.13	-0.08	0.17	-0.05	-0.11	-0.02	0.04	0.07	0.01	0.13	0.02	0.63
MISC54	0.01	-0.04	-0.04	0.13	-0.01	0.71	-0.01	-0.01	0.07	0.01	-0.12	0.09
MISC55	-0.03	-0.02	-0.07	-0.07	0.06	0.88	0.01	0.03	0.00	-0.03	0.03	-0.06
MISC56	-0.05	-0.05	0.11	0.00	-0.01	0.78	0.01	-0.04	-0.05	0.00	0.08	0.05
MISC59	0.06	0.17	0.07	0.09	0.00	0.03	-0.04	0.35	0.00	0.16	0.37	0.13
MISC60	0.03	0.11	0.00	0.05	0.00	0.07	-0.04	0.03	0.11	0.02	0.65	0.02
MISC61	0.01	0.18	0.03	0.01	0.02	-0.04	0.06	0.14	0.15	-0.06	0.66	-0.09
MISC62	0.01	-0.04	-0.03	0.40	0.43	0.00	-0.02	-0.02	0.04	0.03	0.17	0.10
MISC64	-0.15	-0.03	0.06	0.80	-0.03	0.00	0.08	0.05	-0.03	-0.02	-0.02	-0.03
MISC65	-0.09	-0.05	-0.03	0.69	0.11	0.00	0.03	0.05	-0.01	0.13	-0.01	0.08
MISC66	0.23	-0.05	-0.02	0.58	-0.08	0.20	0.00	0.05	-0.06	0.10	0.02	0.02
MISC67	0.20	-0.13	0.04	0.55	-0.01	0.15	0.00	0.06	-0.05	-0.03	0.08	0.03
MISC68	-0.08	0.08	0.21	0.09	0.02	0.17	0.02	0.06	0.05	0.08	0.03	-0.06

2.2.6.4.1 12 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
17	PA1	0.86	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
18	PA1	0.81	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
19	PA1	0.87	FEAR24	When an unfamiliar person tries to touch or pet the dog
20	PA1	0.32	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
21	PA1	0.45	FEAR26	When examined/treated by a veterinarian
23	PA1	0.53	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
27	PA10	0.29	IMP48	Becomes frustrated/impatient in a wide range of situations
28	PA10	0.70	MISC52	Begs persistently for food when people are eating
29	PA10	0.63	MISC53	Steals food
33	PA11	0.37	MISC59	Hyperactive, restless, has trouble settling down
34	PA11	0.65	MISC60	Playful, puppyish, boisterous
35	PA11	0.66	MISC61	Active, energetic, always on the go
37	PA12	0.80	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
38	PA12	0.69	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
39	PA12	0.58	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
40	PA12	0.55	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
52	PA12	0.61	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
53	PA12	0.12	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
42	PA2	0.50	PLAY43	Eagerly engages in play with new/unfamiliar people
43	PA2	0.85	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
44	PA2	0.83	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
45	PA2	0.77	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
26	PA3	0.38	IMP47	Impulsive; doesn’t seem to think before s/he acts
49	PA3	0.60	TRAIN01	Is hard to recall when off the leash
50	PA3	0.59	TRAIN03	Is slow to obey a ‘stay’ command
51	PA3	0.63	TRAIN04	Has difficulty attending/listening to things you say or do
3	PA4	0.81	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.86	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.99	AGG13	When his/her food is taken away by you or another familiar person
12	PA4	0.44	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
41	PA4	0.21	MISC68	Chases own tail/hind end
8	PA5	0.82	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA5	0.81	AGG18	When barked, growled, or lunged at by another dog
11	PA5	0.62	AGG19	Towards other familiar dogs
22	PA5	0.51	FEAR27	When approached directly by an unfamiliar dog
25	PA5	0.41	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
36	PA5	0.43	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
1	PA6	0.65	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA6	0.71	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA6	0.62	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA6	0.70	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA6	0.34	AGG17	When stared at directly by you or another familiar person
13	PA7	0.63	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
14	PA7	0.70	EXCITE36	Excitable when playing with you or other familiar persons
15	PA7	0.80	EXCITE37	Excitable just before being taken out for a walk
16	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
24	PA8	0.20	FEAR30	When groomed or bathed
46	PA8	0.82	SEPR32	Restlessness/agitation/pacing when left alone
47	PA8	0.76	SEPR33	Barking or whining when left alone
48	PA8	0.81	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
30	PA9	0.71	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
31	PA9	0.88	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
32	PA9	0.78	MISC56	Nervous or frightened when ascending or descending some types of stairs

2.2.7 12 Model Reliability Measures

2.3 13 Factors

2.3.1 Imputation of Missing Items (13 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.3.2 13-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.3.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum13, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1242 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.3.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8463937

2.3.3 13-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.3.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF13, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1242 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.3.3.2 13-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8463937

2.3.4 Between-Item Correlations

2.3.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.899.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.692. The maximum correlation was 0.903.

2.3.5 Estimating Number of Factors

2.3.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF13, n.obs = nrow(imputedNumericDF13), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 12.

2.3.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

Number of Factors	MAP value
1	0.0317
2	0.0273
3	0.0220
4	0.0203
5	0.0192
6	0.0178
7	0.0173
8	0.0174
9	0.0157
10	0.0150
11	0.0152
12	0.0151
13	0.0156
14	0.0167
15	0.0173
16	0.0176
17	0.0180
18	0.0189

2.3.6 Factor Analysis for 13 Factors

2.3.6.1 13 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1242 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.0849884^{4}
  
• degrees of freedom: 767
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0736639. Should be > 0.9; need reference)

2.3.6.2 13 Factor Model Communalities

	fanal13.communality
TRAIN01	0.51
TRAIN03	0.40
TRAIN04	0.59
TRAIN07	0.63
TRAIN08	0.62
AGG09	0.73
AGG10	0.68
AGG11	0.76
AGG12	0.80
AGG13	1.00
AGG14	0.49
AGG15	0.78
AGG16	0.78
AGG17	0.67
AGG18	0.74
AGG19	0.66
AGG20	0.50
FEAR21	0.82
FEAR23	0.81
FEAR24	0.86
FEAR25	0.43
FEAR26	0.44
FEAR27	0.85
FEAR28	0.66
FEAR29	0.50
FEAR30	0.64
FEAR31	0.70
SEPR32	0.68
SEPR33	0.60
SEPR34	0.74
EXCITE35	0.49
EXCITE36	0.61
EXCITE37	0.61
EXCITE38	0.63
PLAY43	0.56
PLAY44	0.81
PLAY45	0.76
PLAY46	0.71
IMP47	0.47
IMP48	0.45
MISC52	0.48
MISC53	0.50
MISC54	0.65
MISC55	0.72
MISC56	0.60
MISC59	0.52
MISC61	0.43
MISC62	0.42
MISC64	0.64
MISC65	0.64
MISC66	0.70
MISC67	0.61
MISC68	0.21

2.3.6.3 How many communalities < 0.40?

There are 1 items with communality < 0.40.

	fanal13.communality	item
MISC68	0.21	MISC68

2.3.6.4 13 Factor Model Loadings

	PA2	PA1	PA12	PA4	PA13	PA9	PA7	PA8	PA5	PA6	PA3	PA11	PA10
TRAIN01	-0.10	-0.11	0.09	-0.03	0.03	-0.07	-0.04	0.00	0.02	0.00	0.64	0.09	-0.01
TRAIN03	-0.09	0.04	-0.02	-0.10	-0.07	0.06	0.09	0.07	0.12	-0.12	0.55	0.07	0.10
TRAIN04	-0.03	0.07	0.24	0.06	-0.07	0.01	0.02	0.01	-0.03	0.02	0.63	-0.06	0.00
TRAIN07	-0.12	0.04	0.59	0.02	-0.09	-0.04	0.00	0.02	0.00	0.03	0.30	0.01	-0.06
TRAIN08	-0.71	-0.01	0.11	0.02	-0.01	0.06	0.05	0.02	-0.10	0.08	0.08	0.00	0.02
AGG09	0.07	0.33	0.04	0.06	0.62	0.05	-0.06	-0.04	0.16	-0.06	0.07	-0.04	0.00
AGG10	0.07	0.00	0.00	0.07	0.73	-0.04	-0.02	0.10	0.13	0.01	-0.07	0.00	-0.01
AGG11	-0.08	-0.02	-0.16	0.77	-0.01	-0.02	-0.10	0.10	0.07	0.03	0.18	0.07	-0.01
AGG12	-0.08	0.07	0.05	0.88	-0.03	0.04	0.04	0.01	0.05	-0.01	-0.12	-0.07	0.03
AGG13	0.03	0.01	0.06	0.97	0.07	-0.01	0.04	-0.06	-0.02	0.01	0.00	0.04	0.00
AGG14	-0.03	0.03	0.07	-0.05	0.64	0.01	0.05	0.10	0.10	0.02	-0.06	-0.01	0.06
AGG15	-0.02	0.31	0.00	0.10	0.66	0.01	-0.02	-0.04	0.14	-0.11	0.01	0.06	0.01
AGG16	-0.05	-0.03	0.04	-0.03	0.19	0.07	-0.01	-0.06	0.73	0.20	0.04	-0.05	-0.03
AGG17	0.10	-0.02	0.05	0.20	0.41	0.09	0.12	0.13	-0.04	0.06	0.07	0.19	-0.46
AGG18	0.02	-0.08	0.00	-0.02	0.21	0.00	-0.04	-0.01	0.71	0.19	0.04	0.00	0.00
AGG19	0.05	-0.04	0.00	0.19	-0.01	0.02	0.11	0.04	0.69	-0.02	-0.01	0.12	-0.09
AGG20	-0.02	-0.07	-0.04	0.38	-0.10	0.03	0.00	0.04	0.49	-0.04	-0.03	0.16	0.06
FEAR21	-0.02	0.79	-0.02	0.05	0.10	0.03	0.01	0.01	-0.04	0.10	0.02	0.11	-0.03
FEAR23	-0.02	0.76	0.01	0.02	0.14	0.07	0.00	0.06	-0.02	0.15	-0.02	-0.04	-0.04
FEAR24	-0.10	0.80	0.00	0.06	0.12	-0.02	0.04	-0.01	-0.04	0.17	-0.03	0.04	-0.02
FEAR25	0.02	0.26	0.17	0.11	-0.07	0.32	0.03	0.04	-0.02	0.13	0.12	0.01	-0.03
FEAR26	0.05	0.35	-0.01	0.05	0.01	-0.02	0.00	0.05	0.01	0.09	0.01	0.42	0.02
FEAR27	0.02	0.16	0.01	0.03	-0.04	0.01	-0.01	0.02	0.13	0.83	-0.03	-0.01	0.00
FEAR28	0.03	0.48	0.11	0.00	-0.11	0.37	0.06	0.02	-0.02	0.05	0.02	0.20	-0.08
FEAR29	0.00	-0.01	0.00	-0.03	0.03	-0.04	0.01	0.02	-0.02	0.05	0.05	0.70	-0.01
FEAR30	0.05	0.02	0.05	0.02	-0.06	0.08	-0.03	0.06	0.07	-0.01	-0.03	0.73	0.05
FEAR31	0.00	0.09	0.03	-0.03	-0.10	0.04	0.01	0.02	0.05	0.75	0.00	0.08	0.04
SEPR32	-0.05	0.12	0.01	-0.06	-0.02	-0.05	0.08	0.78	0.08	-0.04	-0.08	0.07	-0.03
SEPR33	-0.02	-0.04	0.06	0.06	-0.04	0.01	0.00	0.76	-0.02	0.02	-0.04	0.01	0.05
SEPR34	-0.01	-0.10	-0.03	-0.01	0.10	0.06	-0.03	0.84	-0.10	0.06	0.10	0.00	-0.05
EXCITE35	-0.12	0.12	0.04	-0.11	0.00	-0.09	0.65	0.15	0.05	-0.02	-0.02	-0.02	0.06
EXCITE36	0.19	0.01	0.06	0.02	0.01	0.01	0.71	-0.05	-0.03	-0.07	-0.04	0.03	-0.04
EXCITE37	-0.08	-0.02	-0.02	0.02	0.01	-0.02	0.80	0.01	0.03	0.02	0.01	-0.02	0.00
EXCITE38	0.03	-0.04	-0.13	0.05	-0.03	0.07	0.77	-0.04	-0.01	0.04	0.06	0.01	-0.01
PLAY43	0.54	-0.30	0.03	0.00	-0.23	0.01	0.08	-0.04	-0.09	0.10	-0.08	-0.05	0.07
PLAY44	0.87	0.00	0.00	-0.02	-0.06	-0.03	0.05	-0.02	0.07	0.00	0.01	0.04	-0.06
PLAY45	0.84	-0.02	0.00	-0.08	0.08	-0.04	0.02	-0.05	-0.07	0.06	-0.09	0.01	0.02
PLAY46	0.76	-0.05	-0.16	0.00	0.12	0.02	0.03	0.03	-0.06	-0.05	0.06	-0.03	-0.07
IMP47	0.33	0.08	-0.02	0.03	0.02	0.03	0.14	0.07	0.03	0.05	0.36	0.00	0.35
IMP48	0.26	0.04	0.08	0.19	-0.02	0.04	0.12	0.11	0.05	0.03	0.21	-0.02	0.38
MISC52	-0.20	-0.19	0.02	0.01	0.24	0.05	0.10	-0.05	-0.17	0.17	0.01	0.18	0.50
MISC53	-0.13	-0.19	-0.04	0.17	0.08	-0.01	0.03	0.04	-0.13	0.06	0.11	0.14	0.55
MISC54	-0.08	-0.02	0.12	-0.06	0.01	0.69	0.05	-0.05	-0.01	0.01	0.00	0.15	0.02
MISC55	0.00	0.00	-0.06	-0.06	-0.01	0.87	0.00	0.05	0.06	-0.02	-0.04	-0.03	-0.03
MISC56	-0.01	-0.04	0.01	0.12	0.02	0.76	-0.04	-0.01	-0.04	0.03	0.01	-0.05	0.05
MISC59	0.29	0.15	0.15	0.04	-0.10	0.02	0.04	0.39	0.09	-0.12	0.10	-0.01	0.32
MISC61	0.39	0.11	0.07	-0.02	0.00	-0.09	0.22	0.23	0.07	-0.15	-0.04	-0.14	0.13
MISC62	0.01	-0.04	0.40	-0.05	0.02	-0.02	0.06	0.01	0.31	0.22	0.06	-0.01	0.11
MISC64	-0.03	-0.17	0.78	0.06	0.10	-0.01	-0.03	0.05	-0.06	0.04	0.02	0.02	-0.09
MISC65	-0.05	-0.11	0.68	-0.04	0.04	0.00	-0.01	0.03	0.09	0.06	0.13	0.07	0.04
MISC66	-0.05	0.24	0.60	-0.02	-0.03	0.20	-0.06	0.03	-0.03	-0.03	0.06	0.06	0.07
MISC67	-0.10	0.22	0.59	0.03	-0.02	0.15	-0.04	0.05	0.04	-0.02	-0.07	0.04	0.09
MISC68	0.11	-0.13	0.05	0.26	0.07	0.18	0.05	0.13	-0.08	0.14	0.15	-0.13	-0.13

2.3.6.4.1 13 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
17	PA1	0.79	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
18	PA1	0.76	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
19	PA1	0.80	FEAR24	When an unfamiliar person tries to touch or pet the dog
23	PA1	0.48	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
28	PA10	0.38	IMP48	Becomes frustrated/impatient in a wide range of situations
29	PA10	0.50	MISC52	Begs persistently for food when people are eating
30	PA10	0.55	MISC53	Steals food
21	PA11	0.42	FEAR26	When examined/treated by a veterinarian
24	PA11	0.70	FEAR29	When having nails trimmed, or feet touched/handled
25	PA11	0.73	FEAR30	When groomed or bathed
36	PA12	0.40	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
37	PA12	0.78	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
38	PA12	0.68	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
39	PA12	0.60	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
40	PA12	0.59	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
52	PA12	0.59	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
53	PA12	0.11	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
1	PA13	0.62	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA13	0.73	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA13	0.64	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA13	0.66	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA13	0.41	AGG17	When stared at directly by you or another familiar person
35	PA2	0.39	MISC61	Active, energetic, always on the go
42	PA2	0.54	PLAY43	Eagerly engages in play with new/unfamiliar people
43	PA2	0.87	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
44	PA2	0.84	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
45	PA2	0.76	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
27	PA3	0.36	IMP47	Impulsive; doesn’t seem to think before s/he acts
49	PA3	0.64	TRAIN01	Is hard to recall when off the leash
50	PA3	0.55	TRAIN03	Is slow to obey a ‘stay’ command
51	PA3	0.63	TRAIN04	Has difficulty attending/listening to things you say or do
3	PA4	0.77	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.88	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.97	AGG13	When his/her food is taken away by you or another familiar person
41	PA4	0.26	MISC68	Chases own tail/hind end
8	PA5	0.73	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA5	0.71	AGG18	When barked, growled, or lunged at by another dog
11	PA5	0.69	AGG19	Towards other familiar dogs
12	PA5	0.49	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
22	PA6	0.83	FEAR27	When approached directly by an unfamiliar dog
26	PA6	0.75	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
13	PA7	0.65	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
14	PA7	0.71	EXCITE36	Excitable when playing with you or other familiar persons
15	PA7	0.80	EXCITE37	Excitable just before being taken out for a walk
16	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
34	PA8	0.39	MISC59	Hyperactive, restless, has trouble settling down
46	PA8	0.78	SEPR32	Restlessness/agitation/pacing when left alone
47	PA8	0.76	SEPR33	Barking or whining when left alone
48	PA8	0.84	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
20	PA9	0.32	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
31	PA9	0.69	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
32	PA9	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
33	PA9	0.76	MISC56	Nervous or frightened when ascending or descending some types of stairs

2.3.7 13 Model Reliability Measures

2.4 14 Factors

2.4.1 Imputation of Missing Items (14 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.4.2 14-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.4.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum14, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1322 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 5.9267723^{4} with 1485 DF, p = 0e+00.

2.4.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8462795

2.4.3 14-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.4.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF14, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1321 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1485 DF, p = NaN.

2.4.3.2 14-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8462795

2.4.4 Between-Item Correlations

2.4.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.9.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.692. The maximum correlation was 0.903.

2.4.5 Estimating Number of Factors

2.4.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF14, n.obs = nrow(imputedNumericDF14), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 12.

2.4.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

Number of Factors	MAP value
1	0.0314
2	0.0270
3	0.0212
4	0.0195
5	0.0186
6	0.0170
7	0.0167
8	0.0160
9	0.0154
10	0.0149
11	0.0150
12	0.0149
13	0.0153
14	0.0156
15	0.0161
16	0.0169
17	0.0169
18	0.0178

2.4.6 Factor Analysis for 14 Factors

2.4.6.1 14 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1321 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.1103584^{4}
  
• degrees of freedom: 806
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0848088. Should be > 0.9; need reference)

2.4.6.2 14 Factor Model Communalities

	fanal14.communality
TRAIN01	0.60
TRAIN03	0.35
TRAIN04	0.54
TRAIN07	0.62
TRAIN08	0.64
AGG09	0.74
AGG10	0.68
AGG11	0.80
AGG12	0.83
AGG13	1.00
AGG14	0.51
AGG15	0.79
AGG16	0.77
AGG17	0.71
AGG18	0.74
AGG19	0.65
AGG20	0.54
FEAR21	0.82
FEAR23	0.81
FEAR24	0.86
FEAR25	0.44
FEAR26	0.44
FEAR27	0.85
FEAR28	0.66
FEAR29	0.54
FEAR30	0.65
FEAR31	0.69
SEPR32	0.68
SEPR33	0.60
SEPR34	0.77
EXCITE35	0.49
EXCITE36	0.61
EXCITE37	0.61
EXCITE38	0.64
PLAY43	0.56
PLAY44	0.81
PLAY45	0.76
PLAY46	0.71
IMP47	0.49
IMP48	0.46
MISC51	0.39
MISC52	0.47
MISC53	0.52
MISC54	0.65
MISC55	0.71
MISC56	0.64
MISC59	0.52
MISC60	0.61
MISC61	0.71
MISC62	0.45
MISC64	0.63
MISC65	0.64
MISC66	0.71
MISC67	0.60
MISC68	0.23

2.4.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

	fanal14.communality	item
TRAIN03	0.35	TRAIN03
MISC51	0.39	MISC51
MISC68	0.23	MISC68

2.4.6.4 14 Factor Model Loadings

	PA2	PA1	PA3	PA4	PA5	PA9	PA8	PA13	PA7	PA6	PA12	PA10	PA11	PA14
TRAIN01	-0.09	-0.06	0.11	-0.05	-0.01	-0.05	-0.01	0.04	-0.03	-0.01	0.70	0.08	0.00	0.02
TRAIN03	-0.06	0.07	0.08	-0.09	-0.10	0.04	0.05	0.14	0.09	-0.14	0.44	0.08	0.02	0.14
TRAIN04	0.02	0.12	0.35	0.06	-0.11	0.00	0.02	0.00	0.03	-0.02	0.53	-0.06	-0.05	0.07
TRAIN07	-0.10	0.05	0.64	0.02	-0.10	-0.05	0.02	0.01	0.01	0.02	0.24	0.02	-0.02	-0.03
TRAIN08	-0.72	-0.01	0.10	0.03	-0.01	0.07	0.01	-0.11	0.05	0.08	0.09	0.02	0.00	-0.01
AGG09	0.04	0.31	0.04	0.07	0.63	0.06	-0.07	0.15	-0.08	-0.04	0.06	0.00	0.09	-0.03
AGG10	0.09	0.00	0.01	0.08	0.73	-0.05	0.10	0.14	-0.02	0.00	-0.08	0.00	-0.04	0.01
AGG11	-0.11	-0.01	-0.17	0.78	-0.03	0.00	0.08	0.08	-0.11	0.03	0.21	0.09	0.08	-0.04
AGG12	-0.04	0.07	0.08	0.88	-0.02	0.02	0.02	0.05	0.05	-0.01	-0.16	-0.07	-0.07	0.06
AGG13	0.02	0.00	0.05	0.96	0.08	-0.01	-0.07	-0.02	0.04	0.02	0.00	0.06	0.01	0.01
AGG14	0.02	0.04	0.08	-0.06	0.63	-0.01	0.12	0.11	0.06	0.00	-0.07	-0.04	-0.12	0.11
AGG15	-0.05	0.29	-0.02	0.10	0.67	0.02	-0.06	0.14	-0.03	-0.10	0.03	0.08	0.07	-0.01
AGG16	-0.04	-0.03	0.05	-0.04	0.19	0.06	-0.06	0.73	-0.01	0.20	0.02	-0.04	-0.01	-0.03
AGG17	0.18	0.01	0.05	0.19	0.39	0.09	0.18	-0.03	0.16	0.05	0.14	0.15	-0.25	-0.40
AGG18	0.01	-0.08	0.00	-0.03	0.21	0.00	-0.02	0.71	-0.04	0.19	0.04	0.01	0.04	-0.01
AGG19	0.05	-0.04	-0.04	0.17	0.00	0.03	0.05	0.69	0.11	-0.01	0.03	0.10	0.00	-0.09
AGG20	0.05	-0.05	-0.04	0.36	-0.12	0.02	0.08	0.52	0.02	-0.07	-0.03	0.11	-0.15	0.11
FEAR21	-0.02	0.79	-0.03	0.05	0.10	0.04	0.01	-0.04	0.01	0.09	0.02	0.10	0.02	-0.03
FEAR23	-0.02	0.76	0.02	0.02	0.14	0.06	0.07	-0.01	0.00	0.15	-0.03	-0.05	-0.01	-0.03
FEAR24	-0.11	0.79	-0.01	0.06	0.12	-0.02	-0.01	-0.05	0.04	0.17	-0.03	0.04	0.01	-0.03
FEAR25	0.06	0.30	0.20	0.10	-0.09	0.30	0.06	-0.01	0.04	0.10	0.09	-0.01	-0.09	0.02
FEAR26	0.03	0.34	-0.01	0.06	0.01	-0.02	0.03	0.01	0.00	0.09	0.00	0.44	0.03	0.01
FEAR27	0.02	0.16	0.00	0.03	-0.05	0.01	0.02	0.13	-0.01	0.82	-0.03	0.01	-0.02	0.01
FEAR28	0.06	0.50	0.14	0.00	-0.11	0.35	0.03	-0.01	0.07	0.03	-0.02	0.18	-0.08	-0.05
FEAR29	-0.03	-0.03	-0.02	-0.02	0.03	-0.03	-0.01	-0.04	0.00	0.05	0.05	0.74	0.05	-0.03
FEAR30	0.05	0.01	0.05	0.02	-0.06	0.07	0.06	0.06	-0.02	-0.02	-0.06	0.74	-0.05	0.06
FEAR31	0.01	0.11	0.04	-0.01	-0.11	0.04	0.02	0.06	0.01	0.73	-0.01	0.09	-0.05	0.05
SEPR32	-0.04	0.13	0.02	-0.06	-0.02	-0.06	0.78	0.09	0.08	-0.04	-0.11	0.07	0.01	-0.02
SEPR33	-0.02	-0.03	0.09	0.06	-0.05	-0.01	0.74	-0.01	0.00	0.01	-0.08	0.03	0.05	0.06
SEPR34	-0.01	-0.08	-0.04	-0.02	0.08	0.07	0.85	-0.09	-0.04	0.06	0.12	-0.01	0.03	-0.04
EXCITE35	-0.16	0.10	0.03	-0.11	0.01	-0.08	0.13	0.05	0.63	0.00	-0.03	-0.01	0.12	0.03
EXCITE36	0.15	-0.01	0.04	0.02	0.02	0.02	-0.06	-0.04	0.69	-0.05	-0.04	0.04	0.12	-0.06
EXCITE37	-0.08	-0.01	-0.02	0.01	0.01	-0.03	0.01	0.03	0.80	0.01	0.00	-0.03	0.01	0.01
EXCITE38	0.05	-0.02	-0.11	0.04	-0.05	0.06	-0.03	0.00	0.77	0.02	0.04	-0.01	-0.02	0.03
PLAY43	0.49	-0.31	0.02	0.00	-0.22	0.01	-0.05	-0.10	0.07	0.11	-0.09	-0.04	0.11	0.06
PLAY44	0.84	-0.01	0.00	-0.02	-0.05	-0.04	-0.02	0.07	0.05	0.00	0.01	0.03	0.07	-0.05
PLAY45	0.80	-0.03	-0.02	-0.08	0.08	-0.04	-0.06	-0.08	0.01	0.08	-0.09	0.01	0.11	0.01
PLAY46	0.76	-0.03	-0.15	0.00	0.11	0.01	0.04	-0.06	0.04	-0.05	0.08	-0.04	0.02	-0.04
IMP47	0.34	0.12	0.02	0.02	0.01	0.02	0.07	0.05	0.14	0.03	0.32	-0.02	0.04	0.40
IMP48	0.28	0.07	0.14	0.17	-0.03	0.02	0.11	0.07	0.12	0.01	0.13	-0.02	0.02	0.43
MISC51	-0.09	-0.10	0.00	0.02	0.08	0.03	0.28	0.03	0.05	0.00	0.40	-0.07	0.06	0.15
MISC52	-0.19	-0.18	0.00	0.01	0.23	0.05	-0.04	-0.16	0.09	0.17	0.02	0.16	-0.01	0.51
MISC53	-0.12	-0.17	-0.07	0.15	0.09	-0.01	0.06	-0.13	0.03	0.07	0.13	0.12	-0.01	0.57
MISC54	-0.05	0.00	0.13	-0.07	0.00	0.68	-0.03	0.00	0.07	0.00	-0.01	0.13	-0.11	0.05
MISC55	-0.01	0.00	-0.06	-0.07	-0.01	0.87	0.04	0.07	-0.01	-0.02	-0.05	-0.02	0.02	-0.03
MISC56	-0.06	-0.05	-0.01	0.12	0.02	0.79	-0.03	-0.04	-0.05	0.04	0.02	-0.02	0.08	0.02
MISC59	0.19	0.12	0.14	0.04	-0.08	0.03	0.34	0.08	0.00	-0.09	0.07	0.04	0.30	0.25
MISC60	0.06	-0.01	0.03	0.01	-0.03	0.06	0.01	-0.06	0.09	0.02	0.02	0.03	0.73	0.02
MISC61	0.14	0.04	-0.01	0.02	0.03	-0.04	0.12	0.05	0.13	-0.10	-0.04	-0.03	0.70	-0.05
MISC62	-0.06	-0.08	0.38	-0.04	0.03	0.00	-0.03	0.30	0.03	0.25	0.05	0.03	0.20	0.05
MISC64	-0.06	-0.19	0.75	0.07	0.11	0.00	0.05	-0.07	-0.03	0.05	0.02	0.03	0.04	-0.11
MISC65	-0.06	-0.12	0.69	-0.04	0.05	0.00	0.04	0.08	-0.01	0.07	0.11	0.07	0.01	0.04
MISC66	-0.03	0.24	0.63	-0.02	-0.01	0.19	0.05	-0.03	-0.06	-0.03	0.02	0.04	-0.03	0.09
MISC67	-0.11	0.20	0.58	0.03	0.00	0.14	0.06	0.03	-0.04	-0.01	-0.10	0.04	0.02	0.08
MISC68	0.07	-0.12	0.05	0.26	0.06	0.20	0.11	-0.08	0.04	0.14	0.17	-0.12	0.08	-0.13

2.4.6.4.1 14 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
17	PA1	0.79	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
18	PA1	0.76	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
19	PA1	0.79	FEAR24	When an unfamiliar person tries to touch or pet the dog
23	PA1	0.50	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
21	PA10	0.44	FEAR26	When examined/treated by a veterinarian
24	PA10	0.74	FEAR29	When having nails trimmed, or feet touched/handled
25	PA10	0.74	FEAR30	When groomed or bathed
36	PA11	0.73	MISC60	Playful, puppyish, boisterous
37	PA11	0.70	MISC61	Active, energetic, always on the go
29	PA12	0.40	MISC51	Escapes or would escape from home, yard or kennel given the chance
51	PA12	0.70	TRAIN01	Is hard to recall when off the leash
52	PA12	0.44	TRAIN03	Is slow to obey a ‘stay’ command
53	PA12	0.53	TRAIN04	Has difficulty attending/listening to things you say or do
8	PA13	0.73	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA13	0.71	AGG18	When barked, growled, or lunged at by another dog
11	PA13	0.69	AGG19	Towards other familiar dogs
12	PA13	0.52	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
27	PA14	0.40	IMP47	Impulsive; doesn’t seem to think before s/he acts
28	PA14	0.43	IMP48	Becomes frustrated/impatient in a wide range of situations
30	PA14	0.51	MISC52	Begs persistently for food when people are eating
31	PA14	0.57	MISC53	Steals food
44	PA2	0.49	PLAY43	Eagerly engages in play with new/unfamiliar people
45	PA2	0.84	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
46	PA2	0.80	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
47	PA2	0.76	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
38	PA3	0.38	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
39	PA3	0.75	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
40	PA3	0.69	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
41	PA3	0.63	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
42	PA3	0.58	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
54	PA3	0.64	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
55	PA3	0.10	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
3	PA4	0.78	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.88	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.96	AGG13	When his/her food is taken away by you or another familiar person
43	PA4	0.26	MISC68	Chases own tail/hind end
1	PA5	0.63	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA5	0.73	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA5	0.63	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA5	0.67	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA5	0.39	AGG17	When stared at directly by you or another familiar person
22	PA6	0.82	FEAR27	When approached directly by an unfamiliar dog
26	PA6	0.73	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
13	PA7	0.63	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
14	PA7	0.69	EXCITE36	Excitable when playing with you or other familiar persons
15	PA7	0.80	EXCITE37	Excitable just before being taken out for a walk
16	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
35	PA8	0.34	MISC59	Hyperactive, restless, has trouble settling down
48	PA8	0.78	SEPR32	Restlessness/agitation/pacing when left alone
49	PA8	0.74	SEPR33	Barking or whining when left alone
50	PA8	0.85	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
20	PA9	0.30	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
32	PA9	0.68	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
33	PA9	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
34	PA9	0.79	MISC56	Nervous or frightened when ascending or descending some types of stairs

2.4.7 14 Model Reliability Measures

2.5 15 Factors

2.5.1 Imputation of Missing Items (15 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.5.2 15-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.5.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum15, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1503 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1711 DF, p = NaN.

2.5.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8475668

2.5.3 15-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.5.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF15, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1502 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1711 DF, p = NaN.

2.5.3.2 15-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8475668

2.5.4 Between-Item Correlations

2.5.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.895.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.897.

2.5.5 Estimating Number of Factors

2.5.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF15, n.obs = nrow(imputedNumericDF15), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 14.

2.5.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

Number of Factors	MAP value
1	0.0286
2	0.0248
3	0.0194
4	0.0176
5	0.0168
6	0.0155
7	0.0150
8	0.0143
9	0.0142
10	0.0143
11	0.0140
12	0.0136
13	0.0138
14	0.0141
15	0.0146
16	0.0145
17	0.0150
18	0.0157

2.5.6 Factor Analysis for 15 Factors

2.5.6.1 15 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1502 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.1602564^{4}
  
• degrees of freedom: 931
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0677907. Should be > 0.9; need reference)

2.5.6.2 15 Factor Model Communalities

	fanal15.communality
TRAIN01	0.54
TRAIN02	0.40
TRAIN03	0.57
TRAIN04	0.60
TRAIN07	0.62
TRAIN08	0.64
AGG09	0.75
AGG10	0.72
AGG11	0.75
AGG12	0.90
AGG13	0.98
AGG14	0.52
AGG15	0.77
AGG16	0.77
AGG17	0.79
AGG18	0.73
AGG19	0.73
AGG20	0.57
FEAR21	0.84
FEAR22	0.41
FEAR23	0.81
FEAR24	0.86
FEAR25	0.50
FEAR26	0.45
FEAR27	0.85
FEAR28	0.66
FEAR29	0.53
FEAR30	0.59
FEAR31	0.69
SEPR32	0.67
SEPR33	0.67
SEPR34	0.74
EXCITE35	0.50
EXCITE36	0.61
EXCITE37	0.60
EXCITE38	0.64
ATT39	0.29
ATT41	0.25
PLAY43	0.56
PLAY44	0.80
PLAY45	0.76
PLAY46	0.71
IMP47	0.48
IMP48	0.43
MISC51	0.50
MISC52	0.52
MISC53	0.53
MISC54	0.64
MISC55	0.74
MISC56	0.63
MISC59	0.50
MISC60	0.58
MISC61	0.68
MISC62	0.45
MISC64	0.63
MISC65	0.64
MISC66	0.68
MISC67	0.60
MISC69	0.22

2.5.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

	fanal15.communality	item
ATT39	0.29	ATT39
ATT41	0.25	ATT41
MISC69	0.22	MISC69

2.5.6.4 15 Factor Model Loadings

	PA1	PA2	PA12	PA4	PA5	PA9	PA8	PA7	PA15	PA3	PA6	PA11	PA10	PA14	PA13
TRAIN01	-0.05	-0.10	0.16	-0.06	-0.04	-0.08	-0.03	-0.05	0.06	0.45	-0.02	0.11	0.06	0.03	0.35
TRAIN02	-0.05	-0.01	0.02	0.01	0.11	0.04	0.02	0.07	-0.09	0.61	0.04	-0.05	0.10	-0.05	-0.10
TRAIN03	-0.03	-0.07	-0.05	-0.06	0.04	0.05	0.07	0.07	0.07	0.73	-0.08	0.01	0.08	0.02	-0.08
TRAIN04	0.06	0.01	0.29	0.08	-0.06	-0.03	0.01	0.00	-0.06	0.58	0.04	0.00	-0.08	-0.04	0.14
TRAIN07	0.05	-0.10	0.64	0.02	-0.09	-0.07	0.02	0.00	0.01	0.23	0.01	-0.02	0.00	-0.03	0.02
TRAIN08	-0.02	-0.72	0.11	0.03	-0.02	0.07	0.01	0.06	-0.11	0.06	0.07	0.04	0.03	0.01	0.03
AGG09	0.29	0.03	0.04	0.09	0.66	0.07	-0.06	-0.07	0.08	0.05	-0.01	-0.03	-0.01	0.11	0.06
AGG10	-0.03	0.08	-0.02	0.10	0.79	-0.03	0.11	-0.01	0.06	0.00	0.01	0.00	0.03	-0.06	-0.04
AGG11	0.02	-0.12	-0.11	0.70	-0.06	-0.01	0.05	-0.10	0.15	0.03	-0.01	0.07	0.11	0.11	0.21
AGG12	0.02	-0.04	0.02	0.94	0.02	0.03	0.05	0.05	0.01	0.00	0.03	-0.03	-0.08	-0.06	-0.13
AGG13	0.00	0.01	0.05	0.94	0.08	-0.01	-0.06	0.04	0.00	-0.02	0.00	0.04	0.07	0.02	0.05
AGG14	0.09	0.04	0.08	-0.06	0.62	0.00	0.11	0.06	0.10	-0.06	-0.02	0.17	-0.07	-0.15	0.01
AGG15	0.30	-0.05	-0.03	0.11	0.65	0.03	-0.07	-0.04	0.11	0.04	-0.10	-0.01	0.08	0.07	0.09
AGG16	-0.08	-0.05	0.05	-0.02	0.28	0.07	-0.06	-0.02	0.62	0.07	0.29	-0.09	-0.06	0.02	-0.05
AGG17	0.06	0.14	0.13	0.14	0.29	0.09	0.14	0.19	0.03	-0.12	0.01	-0.24	0.17	-0.26	0.45
AGG18	-0.10	0.01	0.03	-0.03	0.28	0.00	-0.02	-0.05	0.63	0.02	0.26	-0.02	-0.02	0.06	0.00
AGG19	0.03	0.05	-0.01	0.10	-0.03	0.01	0.01	0.09	0.78	-0.02	-0.03	-0.06	0.09	0.00	0.07
AGG20	0.01	0.06	-0.01	0.31	-0.12	-0.01	0.05	-0.01	0.60	-0.03	-0.07	0.13	0.08	-0.14	-0.03
FEAR21	0.83	-0.02	-0.01	0.03	0.07	0.02	0.00	0.00	-0.01	-0.02	0.08	-0.01	0.08	0.03	0.05
FEAR22	0.35	-0.01	0.17	-0.06	-0.23	0.22	0.04	0.06	0.20	0.01	-0.10	0.08	0.06	-0.17	-0.16
FEAR23	0.77	-0.01	0.00	0.02	0.14	0.04	0.06	-0.01	-0.02	0.00	0.14	-0.05	-0.05	-0.01	-0.02
FEAR24	0.81	-0.11	-0.02	0.05	0.11	-0.04	-0.03	0.04	-0.03	-0.02	0.14	-0.03	0.06	0.02	-0.02
FEAR25	0.39	0.10	0.23	0.07	-0.15	0.27	0.05	0.03	0.10	0.03	0.02	0.11	-0.05	-0.14	-0.02
FEAR26	0.33	0.03	-0.01	0.05	0.01	-0.03	0.04	-0.01	0.02	0.04	0.10	0.02	0.44	0.04	-0.02
FEAR27	0.14	0.01	-0.02	0.04	-0.04	0.02	0.02	0.00	0.06	-0.02	0.85	0.01	0.01	-0.02	0.01
FEAR28	0.48	0.07	0.13	0.02	-0.10	0.34	0.04	0.06	-0.01	0.05	0.05	-0.08	0.17	-0.08	-0.05
FEAR29	-0.04	-0.02	0.01	-0.02	0.02	-0.01	0.02	0.00	0.00	0.05	0.06	0.05	0.70	0.04	0.03
FEAR30	0.00	0.06	0.04	0.05	-0.06	0.10	0.10	-0.04	0.07	0.04	0.04	0.08	0.65	-0.05	-0.04
FEAR31	0.09	-0.01	0.03	-0.02	-0.10	0.05	0.03	0.02	0.01	0.00	0.75	0.04	0.10	-0.05	-0.01
SEPR32	0.09	-0.04	0.00	-0.04	0.02	-0.06	0.78	0.07	0.06	-0.02	-0.01	-0.07	0.07	0.02	-0.06
SEPR33	-0.10	-0.02	0.03	0.10	0.02	0.01	0.80	-0.02	-0.06	0.07	0.05	-0.02	0.02	0.03	-0.14
SEPR34	-0.03	-0.02	0.00	-0.05	0.02	0.06	0.80	-0.03	-0.03	0.00	0.01	0.05	0.00	0.02	0.21
EXCITE35	0.10	-0.14	0.01	-0.10	0.02	-0.09	0.13	0.63	0.05	0.03	-0.01	0.03	-0.01	0.11	-0.07
EXCITE36	-0.01	0.15	0.03	0.04	0.01	0.01	-0.06	0.69	-0.04	0.01	-0.06	-0.06	0.06	0.10	-0.03
EXCITE37	-0.03	-0.08	-0.02	0.04	0.00	-0.02	0.01	0.78	0.01	0.02	0.04	0.02	-0.03	0.03	0.04
EXCITE38	-0.01	0.06	-0.11	0.05	-0.08	0.06	-0.03	0.77	0.02	0.03	0.02	0.06	-0.02	-0.04	0.05
ATT39	0.08	-0.07	0.10	-0.17	0.17	-0.08	0.08	0.21	0.03	-0.23	-0.03	0.10	0.08	0.16	-0.27
ATT41	0.05	0.05	0.15	0.03	-0.03	-0.03	0.15	0.09	0.07	-0.09	-0.03	0.30	-0.02	0.11	-0.21
PLAY43	-0.31	0.51	0.00	0.01	-0.22	0.02	-0.04	0.08	-0.09	-0.03	0.10	0.03	-0.04	0.08	-0.09
PLAY44	-0.03	0.83	0.00	-0.02	-0.03	-0.03	-0.02	0.05	0.07	0.02	0.01	-0.09	0.04	0.08	0.00
PLAY45	-0.02	0.81	-0.01	-0.08	0.08	-0.05	-0.06	0.02	-0.07	-0.07	0.05	0.00	0.03	0.08	-0.04
PLAY46	-0.02	0.75	-0.13	-0.02	0.08	0.01	0.03	0.04	-0.02	0.00	-0.08	-0.02	-0.04	0.00	0.10
IMP47	0.09	0.35	0.01	0.04	0.02	0.00	0.06	0.11	0.00	0.30	0.10	0.34	-0.06	0.09	0.10
IMP48	0.01	0.29	0.08	0.22	0.03	0.01	0.11	0.09	-0.01	0.25	0.09	0.29	-0.04	0.06	-0.08
MISC51	0.02	-0.08	0.08	-0.05	-0.06	0.00	0.22	0.03	0.14	0.09	-0.06	0.31	-0.11	0.09	0.43
MISC52	-0.06	-0.13	0.04	-0.03	0.14	0.03	-0.07	0.08	-0.06	-0.06	0.06	0.67	0.15	-0.05	-0.05
MISC53	-0.09	-0.08	-0.05	0.13	0.01	-0.02	0.03	0.00	-0.05	0.07	0.02	0.65	0.06	0.00	0.04
MISC54	0.00	-0.05	0.15	-0.05	0.00	0.67	-0.03	0.06	0.00	-0.01	0.01	0.08	0.12	-0.09	0.01
MISC55	0.00	-0.01	-0.08	-0.05	0.01	0.88	0.05	-0.01	0.06	0.02	-0.01	-0.04	-0.02	0.00	-0.04
MISC56	-0.07	-0.08	0.00	0.12	0.03	0.77	-0.04	-0.04	-0.08	0.00	0.07	0.01	0.02	0.12	0.08
MISC59	0.12	0.22	0.13	0.06	-0.10	0.03	0.32	-0.01	0.06	0.08	-0.04	0.18	-0.01	0.32	0.04
MISC60	0.00	0.10	0.05	0.00	-0.04	0.08	0.03	0.11	-0.07	0.01	-0.01	0.02	0.03	0.68	-0.04
MISC61	0.06	0.19	0.01	0.00	0.00	-0.01	0.13	0.16	0.05	-0.06	-0.12	-0.06	-0.04	0.64	0.01
MISC62	-0.08	-0.05	0.39	-0.04	0.04	0.01	-0.04	0.03	0.25	0.04	0.27	0.04	0.01	0.21	0.01
MISC64	-0.15	-0.06	0.79	0.05	0.07	-0.01	0.03	-0.02	-0.05	-0.04	0.01	-0.04	0.03	0.03	0.06
MISC65	-0.08	-0.05	0.71	-0.05	0.02	-0.01	0.02	-0.02	0.09	0.06	0.05	0.08	0.04	0.02	0.06
MISC66	0.24	-0.03	0.60	0.00	-0.01	0.16	0.05	-0.08	-0.04	0.09	-0.02	0.04	0.03	-0.02	-0.07
MISC67	0.22	-0.09	0.58	0.04	-0.01	0.13	0.05	-0.05	0.02	0.00	-0.01	0.03	0.03	0.01	-0.14
MISC69	0.07	0.01	0.12	0.04	-0.01	0.22	0.12	0.06	0.04	-0.05	0.10	0.14	-0.21	0.02	0.18

2.5.6.4.1 15 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
19	PA1	0.83	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20	PA1	0.35	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21	PA1	0.77	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22	PA1	0.81	FEAR24	When an unfamiliar person tries to touch or pet the dog
23	PA1	0.39	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26	PA1	0.48	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
24	PA10	0.44	FEAR26	When examined/treated by a veterinarian
27	PA10	0.70	FEAR29	When having nails trimmed, or feet touched/handled
28	PA10	0.65	FEAR30	When groomed or bathed
14	PA11	0.30	ATT41	Tends to nudge or paw you (or others) for attention
31	PA11	0.29	IMP48	Becomes frustrated/impatient in a wide range of situations
33	PA11	0.67	MISC52	Begs persistently for food when people are eating
34	PA11	0.65	MISC53	Steals food
41	PA12	0.39	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
42	PA12	0.79	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
43	PA12	0.71	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
44	PA12	0.60	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
45	PA12	0.58	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
58	PA12	0.64	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
59	PA12	0.11	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
9	PA13	0.45	AGG17	When stared at directly by you or another familiar person
32	PA13	0.43	MISC51	Escapes or would escape from home, yard or kennel given the chance
39	PA14	0.68	MISC60	Playful, puppyish, boisterous
40	PA14	0.64	MISC61	Active, energetic, always on the go
8	PA15	0.62	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA15	0.63	AGG18	When barked, growled, or lunged at by another dog
11	PA15	0.78	AGG19	Towards other familiar dogs
12	PA15	0.60	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
30	PA2	0.35	IMP47	Impulsive; doesn’t seem to think before s/he acts
47	PA2	0.51	PLAY43	Eagerly engages in play with new/unfamiliar people
48	PA2	0.83	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
49	PA2	0.81	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
50	PA2	0.75	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
54	PA3	0.45	TRAIN01	Is hard to recall when off the leash
55	PA3	0.61	TRAIN02	Is slow to obey a ‘sit’ command
56	PA3	0.73	TRAIN03	Is slow to obey a ‘stay’ command
57	PA3	0.58	TRAIN04	Has difficulty attending/listening to things you say or do
3	PA4	0.70	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.94	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.94	AGG13	When his/her food is taken away by you or another familiar person
1	PA5	0.66	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA5	0.79	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA5	0.62	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA5	0.65	AGG15	When an unfamiliar person tries to touch or pet the dog
25	PA6	0.85	FEAR27	When approached directly by an unfamiliar dog
29	PA6	0.75	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
13	PA7	0.21	ATT39	Displays a strong attachment for you or another familiar person
15	PA7	0.63	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16	PA7	0.69	EXCITE36	Excitable when playing with you or other familiar persons
17	PA7	0.78	EXCITE37	Excitable just before being taken out for a walk
18	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
38	PA8	0.32	MISC59	Hyperactive, restless, has trouble settling down
51	PA8	0.78	SEPR32	Restlessness/agitation/pacing when left alone
52	PA8	0.80	SEPR33	Barking or whining when left alone
53	PA8	0.80	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
35	PA9	0.67	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
36	PA9	0.88	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
37	PA9	0.77	MISC56	Nervous or frightened when ascending or descending some types of stairs
46	PA9	0.22	MISC69	Chases/follows shadows, light spots, etc.

2.5.7 15 Model Reliability Measures

2.6 16 Factors

2.6.1 Imputation of Missing Items (16 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.6.2 16-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.6.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum16, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1647 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.6.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8510013

2.6.3 16-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.6.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF16, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1646 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.6.3.2 16-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8510013

2.6.4 Between-Item Correlations

2.6.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.892.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.892.

2.6.5 Estimating Number of Factors

2.6.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF16, n.obs = nrow(imputedNumericDF16), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 14.

2.6.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

Number of Factors	MAP value
1	0.0275
2	0.0237
3	0.0184
4	0.0167
5	0.0158
6	0.0147
7	0.0142
8	0.0134
9	0.0133
10	0.0131
11	0.0127
12	0.0126
13	0.0129
14	0.0130
15	0.0134
16	0.0137
17	0.0142
18	0.0147

2.6.6 Factor Analysis for 16 Factors

2.6.6.1 16 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1646 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.2319463^{4}
  
• degrees of freedom: 1019
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0665037. Should be > 0.9; need reference)

2.6.6.2 16 Factor Model Communalities

	fanal16.communality
TRAIN01	0.56
TRAIN02	0.43
TRAIN03	0.63
TRAIN04	0.58
TRAIN07	0.62
TRAIN08	0.63
AGG09	0.76
AGG10	0.72
AGG11	0.82
AGG12	0.87
AGG13	0.98
AGG14	0.50
AGG15	0.78
AGG16	0.77
AGG17	0.73
AGG18	0.73
AGG19	0.72
AGG20	0.57
FEAR21	0.84
FEAR22	0.43
FEAR23	0.80
FEAR24	0.86
FEAR25	0.51
FEAR26	0.44
FEAR27	0.86
FEAR28	0.67
FEAR29	0.56
FEAR30	0.62
FEAR31	0.68
SEPR32	0.67
SEPR33	0.64
SEPR34	0.75
EXCITE35	0.50
EXCITE36	0.61
EXCITE37	0.61
EXCITE38	0.64
ATT39	0.30
ATT41	0.27
PLAY43	0.57
PLAY44	0.81
PLAY45	0.78
PLAY46	0.74
IMP47	0.59
IMP48	0.59
IMP49	0.39
MISC50	0.31
MISC51	0.54
MISC52	0.60
MISC53	0.51
MISC54	0.62
MISC55	0.74
MISC56	0.64
MISC59	0.56
MISC60	0.59
MISC61	0.66
MISC62	0.51
MISC63	0.37
MISC64	0.61
MISC65	0.63
MISC66	0.69
MISC67	0.60
MISC68	0.22

2.6.6.3 How many communalities < 0.40?

There are 6 items with communality < 0.40.

	fanal16.communality	item
ATT39	0.30	ATT39
ATT41	0.27	ATT41
IMP49	0.39	IMP49
MISC50	0.31	MISC50
MISC63	0.37	MISC63
MISC68	0.22	MISC68

2.6.6.4 16 Factor Model Loadings

	PA9	PA1	PA2	PA4	PA3	PA7	PA5	PA8	PA6	PA10	PA13	PA12	PA16	PA14	PA11	PA15
TRAIN01	-0.03	0.18	-0.04	-0.05	-0.04	-0.07	-0.09	-0.04	0.06	0.45	-0.03	0.05	0.02	0.00	0.11	0.38
TRAIN02	-0.02	0.03	0.03	0.03	0.08	0.04	0.05	0.02	-0.10	0.63	0.06	0.04	0.00	-0.04	-0.01	-0.09
TRAIN03	0.00	-0.06	-0.02	-0.04	0.00	0.04	0.05	0.06	0.07	0.77	-0.07	0.03	0.03	0.04	0.03	-0.07
TRAIN04	0.04	0.29	-0.04	0.07	-0.05	0.00	-0.02	0.01	-0.08	0.49	0.04	-0.05	0.18	-0.05	-0.09	0.16
TRAIN07	0.05	0.63	-0.09	0.03	-0.09	-0.02	-0.07	0.04	-0.01	0.25	0.02	0.00	0.00	-0.03	-0.02	0.03
TRAIN08	0.00	0.10	-0.68	0.04	-0.02	0.05	0.07	0.02	-0.11	0.10	0.07	0.02	-0.10	0.01	0.07	0.03
AGG09	0.27	0.05	0.01	0.08	0.68	-0.07	0.07	-0.07	0.07	0.02	-0.02	0.00	0.05	0.11	-0.05	0.05
AGG10	-0.04	-0.02	0.08	0.09	0.79	-0.01	-0.02	0.12	0.07	0.01	0.02	0.02	0.00	-0.06	0.02	-0.07
AGG11	0.05	-0.11	-0.04	0.77	-0.07	-0.11	-0.01	0.07	0.14	0.08	0.01	0.07	-0.11	0.11	0.09	0.21
AGG12	0.02	0.03	-0.08	0.89	0.03	0.05	0.03	0.03	0.02	-0.03	0.02	-0.06	0.08	-0.07	-0.04	-0.16
AGG13	0.00	0.05	0.02	0.93	0.09	0.04	-0.01	-0.07	0.00	-0.01	0.00	0.08	0.02	0.00	0.02	0.01
AGG14	0.08	0.08	0.03	-0.05	0.62	0.05	-0.01	0.12	0.10	-0.04	-0.01	-0.06	0.02	-0.13	0.16	-0.01
AGG15	0.29	-0.03	-0.06	0.09	0.67	-0.03	0.03	-0.07	0.11	0.01	-0.10	0.10	0.01	0.05	-0.01	0.08
AGG16	-0.07	0.04	-0.05	-0.02	0.28	-0.02	0.06	-0.05	0.62	0.09	0.28	-0.05	-0.01	0.01	-0.07	-0.06
AGG17	0.07	0.14	0.16	0.15	0.33	0.19	0.08	0.16	0.02	-0.08	0.01	0.19	-0.15	-0.29	-0.20	0.34
AGG18	-0.10	0.02	0.00	-0.03	0.28	-0.05	-0.01	-0.01	0.63	0.02	0.24	0.00	0.03	0.05	-0.03	-0.01
AGG19	0.03	0.00	0.07	0.12	-0.02	0.10	0.02	0.02	0.76	-0.01	-0.01	0.08	-0.04	0.00	-0.05	0.09
AGG20	0.00	-0.03	0.03	0.30	-0.12	-0.01	-0.01	0.06	0.59	-0.04	-0.07	0.09	0.09	-0.15	0.08	-0.03
FEAR21	0.83	-0.02	-0.01	0.04	0.07	0.00	0.01	0.00	-0.01	-0.01	0.08	0.08	0.01	0.03	-0.02	0.04
FEAR22	0.38	0.17	0.03	-0.05	-0.25	0.04	0.21	0.04	0.20	0.05	-0.10	0.04	-0.04	-0.15	0.13	-0.15
FEAR23	0.76	0.01	-0.02	0.01	0.16	-0.01	0.05	0.05	-0.02	-0.02	0.15	-0.05	0.04	0.00	-0.06	-0.01
FEAR24	0.82	-0.02	-0.08	0.06	0.11	0.03	-0.04	-0.02	-0.04	0.00	0.16	0.03	-0.04	0.03	-0.01	-0.02
FEAR25	0.40	0.26	0.13	0.10	-0.15	0.02	0.28	0.04	0.07	0.06	0.04	-0.07	0.00	-0.12	0.13	0.00
FEAR26	0.33	-0.03	0.04	0.06	0.01	-0.01	-0.03	0.04	0.00	0.06	0.10	0.43	-0.01	0.03	0.03	-0.03
FEAR27	0.15	-0.01	0.02	0.04	-0.04	-0.01	0.02	0.03	0.07	-0.02	0.85	0.02	0.01	-0.02	0.02	0.01
FEAR28	0.49	0.13	0.05	-0.01	-0.10	0.06	0.33	0.02	0.00	0.04	0.02	0.18	0.02	-0.09	-0.06	-0.09
FEAR29	-0.05	-0.01	-0.04	-0.02	0.03	0.01	-0.03	0.00	-0.03	0.04	0.05	0.75	-0.02	0.05	0.04	0.01
FEAR30	-0.03	0.03	-0.01	0.03	-0.05	-0.02	0.08	0.07	0.05	-0.01	0.02	0.71	0.08	-0.04	0.03	-0.06
FEAR31	0.10	0.02	-0.02	-0.03	-0.11	0.01	0.05	0.03	0.02	-0.01	0.73	0.10	0.03	-0.06	0.05	-0.02
SEPR32	0.08	0.00	-0.07	-0.05	0.03	0.08	-0.05	0.77	0.07	-0.02	-0.01	0.08	0.04	0.01	-0.07	-0.07
SEPR33	-0.08	0.04	0.00	0.09	0.01	-0.02	0.01	0.76	-0.04	0.10	0.04	0.02	0.01	0.04	0.02	-0.14
SEPR34	-0.03	0.01	0.01	-0.03	0.03	-0.03	0.07	0.80	-0.04	0.01	0.03	0.00	0.01	0.01	0.05	0.21
EXCITE35	0.11	0.01	-0.11	-0.09	0.01	0.62	-0.08	0.15	0.04	0.07	0.00	-0.03	-0.04	0.13	0.06	-0.06
EXCITE36	-0.02	0.03	0.14	0.02	0.01	0.70	0.02	-0.05	-0.04	-0.01	-0.06	0.05	0.02	0.09	-0.06	-0.03
EXCITE37	-0.03	-0.02	-0.09	0.02	0.00	0.79	-0.03	0.01	0.02	0.01	0.03	-0.02	0.03	0.01	0.01	0.03
EXCITE38	-0.01	-0.10	0.04	0.03	-0.07	0.77	0.05	-0.04	0.03	0.01	0.01	-0.01	0.05	-0.04	0.04	0.04
ATT39	0.13	0.08	0.06	-0.09	0.12	0.17	-0.09	0.14	0.01	-0.06	0.01	-0.01	-0.23	0.20	0.22	-0.25
ATT41	0.07	0.13	0.10	0.07	-0.06	0.06	-0.04	0.17	0.06	0.00	-0.02	-0.05	-0.01	0.15	0.33	-0.20
PLAY43	-0.31	0.02	0.51	0.01	-0.23	0.07	0.03	-0.04	-0.09	-0.03	0.10	-0.05	0.02	0.09	0.03	-0.08
PLAY44	-0.02	0.01	0.84	-0.01	-0.04	0.04	-0.04	-0.02	0.07	0.02	0.01	0.04	0.05	0.06	-0.09	-0.01
PLAY45	0.01	0.00	0.85	-0.06	0.05	-0.01	-0.04	-0.04	-0.06	-0.04	0.06	-0.01	0.00	0.08	0.03	-0.05
PLAY46	0.01	-0.11	0.81	0.00	0.08	0.02	0.01	0.04	-0.01	0.04	-0.07	-0.06	-0.01	-0.02	0.00	0.08
IMP47	0.03	-0.06	0.14	-0.05	0.06	0.11	-0.01	0.01	-0.01	0.12	0.06	0.04	0.61	0.02	0.09	0.11
IMP48	-0.07	0.01	0.06	0.12	0.07	0.09	0.00	0.06	-0.01	0.07	0.05	0.05	0.63	0.00	0.06	-0.10
IMP49	0.00	0.10	0.03	0.18	0.01	0.12	-0.06	-0.07	-0.06	0.21	0.08	0.06	0.32	-0.04	0.07	0.14
MISC50	0.01	0.05	0.03	0.27	-0.06	0.09	0.05	0.23	-0.06	0.05	0.07	-0.09	0.16	0.11	-0.02	0.18
MISC51	0.00	0.08	-0.11	-0.06	-0.04	0.04	0.00	0.21	0.13	0.02	-0.06	-0.09	0.19	0.06	0.20	0.50
MISC52	-0.03	0.03	-0.04	0.00	0.12	0.04	0.03	-0.05	-0.06	0.00	0.06	0.07	0.00	-0.04	0.74	0.00
MISC53	-0.07	-0.06	-0.07	0.13	-0.01	-0.02	-0.03	0.03	-0.04	0.06	0.01	0.05	0.15	0.00	0.58	0.09
MISC54	0.02	0.14	-0.05	-0.06	-0.01	0.06	0.65	-0.03	0.00	0.01	0.00	0.12	0.01	-0.10	0.09	0.00
MISC55	0.00	-0.07	0.01	-0.05	0.01	-0.01	0.88	0.05	0.05	0.04	0.01	-0.02	-0.04	0.01	-0.02	-0.04
MISC56	-0.08	-0.02	-0.10	0.10	0.05	-0.03	0.78	-0.03	-0.06	-0.02	0.05	0.03	0.04	0.10	-0.01	0.07
MISC59	0.08	0.10	0.06	-0.01	-0.07	-0.01	0.01	0.30	0.06	-0.05	-0.09	0.07	0.43	0.28	-0.01	0.05
MISC60	0.01	0.05	0.13	0.02	-0.04	0.11	0.08	0.03	-0.08	0.03	-0.01	0.02	0.04	0.67	0.01	0.00
MISC61	0.08	0.00	0.22	0.00	0.01	0.16	-0.02	0.13	0.05	-0.02	-0.14	-0.03	0.04	0.60	-0.06	0.02
MISC62	-0.09	0.44	-0.07	-0.06	0.06	0.04	0.00	-0.08	0.26	-0.01	0.25	0.04	0.07	0.23	0.04	0.03
MISC63	-0.02	0.42	-0.02	0.04	0.02	0.15	0.09	-0.11	0.05	-0.04	0.07	0.00	0.12	0.16	0.13	0.04
MISC64	-0.13	0.77	-0.03	0.06	0.06	-0.04	-0.01	0.06	-0.05	0.01	0.01	0.03	-0.09	0.02	0.01	0.05
MISC65	-0.08	0.69	-0.07	-0.05	0.03	-0.03	-0.02	0.03	0.08	0.06	0.04	0.06	0.06	0.00	0.06	0.06
MISC66	0.22	0.59	-0.09	-0.02	0.00	-0.07	0.17	0.05	-0.05	0.04	-0.03	0.04	0.13	-0.03	0.00	-0.07
MISC67	0.23	0.54	-0.13	0.01	-0.01	-0.06	0.13	0.06	0.04	-0.02	-0.03	0.03	0.09	0.00	0.03	-0.13
MISC68	-0.09	0.09	0.08	0.25	0.03	0.06	0.19	0.11	-0.07	0.02	0.13	-0.09	-0.02	0.05	-0.06	0.21

2.6.6.4.1 16 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
43	PA1	0.44	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
44	PA1	0.42	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
45	PA1	0.77	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
46	PA1	0.69	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
47	PA1	0.59	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
48	PA1	0.54	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
61	PA1	0.63	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
57	PA10	0.45	TRAIN01	Is hard to recall when off the leash
58	PA10	0.63	TRAIN02	Is slow to obey a ‘sit’ command
59	PA10	0.77	TRAIN03	Is slow to obey a ‘stay’ command
60	PA10	0.49	TRAIN04	Has difficulty attending/listening to things you say or do
62	PA10	0.10	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
13	PA11	0.22	ATT39	Displays a strong attachment for you or another familiar person
14	PA11	0.33	ATT41	Tends to nudge or paw you (or others) for attention
35	PA11	0.74	MISC52	Begs persistently for food when people are eating
36	PA11	0.58	MISC53	Steals food
24	PA12	0.43	FEAR26	When examined/treated by a veterinarian
27	PA12	0.75	FEAR29	When having nails trimmed, or feet touched/handled
28	PA12	0.71	FEAR30	When groomed or bathed
25	PA13	0.85	FEAR27	When approached directly by an unfamiliar dog
29	PA13	0.73	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
41	PA14	0.67	MISC60	Playful, puppyish, boisterous
42	PA14	0.60	MISC61	Active, energetic, always on the go
9	PA15	0.34	AGG17	When stared at directly by you or another familiar person
34	PA15	0.50	MISC51	Escapes or would escape from home, yard or kennel given the chance
30	PA16	0.61	IMP47	Impulsive; doesn’t seem to think before s/he acts
31	PA16	0.63	IMP48	Becomes frustrated/impatient in a wide range of situations
32	PA16	0.32	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
40	PA16	0.43	MISC59	Hyperactive, restless, has trouble settling down
50	PA2	0.51	PLAY43	Eagerly engages in play with new/unfamiliar people
51	PA2	0.84	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
52	PA2	0.85	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
53	PA2	0.81	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.68	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.79	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.62	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.67	AGG15	When an unfamiliar person tries to touch or pet the dog
3	PA4	0.77	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.89	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.93	AGG13	When his/her food is taken away by you or another familiar person
33	PA4	0.27	MISC50	NA
49	PA4	0.25	MISC68	Chases own tail/hind end
37	PA5	0.65	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA5	0.88	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA5	0.78	MISC56	Nervous or frightened when ascending or descending some types of stairs
8	PA6	0.62	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA6	0.63	AGG18	When barked, growled, or lunged at by another dog
11	PA6	0.76	AGG19	Towards other familiar dogs
12	PA6	0.59	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
15	PA7	0.62	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16	PA7	0.70	EXCITE36	Excitable when playing with you or other familiar persons
17	PA7	0.79	EXCITE37	Excitable just before being taken out for a walk
18	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
54	PA8	0.77	SEPR32	Restlessness/agitation/pacing when left alone
55	PA8	0.76	SEPR33	Barking or whining when left alone
56	PA8	0.80	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
19	PA9	0.83	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20	PA9	0.38	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21	PA9	0.76	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22	PA9	0.82	FEAR24	When an unfamiliar person tries to touch or pet the dog
23	PA9	0.40	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26	PA9	0.49	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)

2.6.7 16 Model Reliability Measures

2.7 17 Factors

2.7.1 Imputation of Missing Items (17 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.7.2 17-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.7.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum17, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1639 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.7.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.7.3 17-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.7.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF17, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.7.3.2 17-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.7.4 Between-Item Correlations

2.7.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.892.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.893.

2.7.5 Estimating Number of Factors

2.7.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF17, n.obs = nrow(imputedNumericDF17), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 15.

2.7.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

Number of Factors	MAP value
1	0.0272
2	0.0236
3	0.0184
4	0.0167
5	0.0159
6	0.0148
7	0.0144
8	0.0135
9	0.0135
10	0.0132
11	0.0128
12	0.0127
13	0.0130
14	0.0132
15	0.0136
16	0.0139
17	0.0143
18	0.0147

2.7.6 Factor Analysis for 17 Factors

2.7.6.1 17 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.1792997^{4}
  
• degrees of freedom: 973
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.1065804. Should be > 0.9; need reference)

2.7.6.2 17 Factor Model Communalities

	fanal17.communality
TRAIN01	0.56
TRAIN02	0.44
TRAIN03	0.60
TRAIN04	0.58
TRAIN07	0.62
TRAIN08	0.63
AGG09	0.76
AGG10	0.71
AGG11	0.82
AGG12	0.87
AGG13	1.00
AGG14	0.50
AGG15	0.82
AGG16	0.77
AGG17	0.78
AGG18	0.74
AGG19	0.74
AGG20	0.57
FEAR21	0.83
FEAR22	0.43
FEAR23	0.80
FEAR24	0.86
FEAR25	0.51
FEAR26	0.44
FEAR27	0.87
FEAR28	0.67
FEAR29	0.54
FEAR30	0.68
FEAR31	0.68
SEPR32	0.67
SEPR33	0.68
SEPR34	0.75
EXCITE35	0.50
EXCITE36	0.61
EXCITE37	0.60
EXCITE38	0.64
ATT39	0.71
ATT40	0.42
ATT41	0.30
PLAY43	0.59
PLAY44	0.81
PLAY45	0.78
PLAY46	0.74
IMP47	0.61
IMP48	0.61
IMP49	0.39
MISC51	0.52
MISC52	0.57
MISC53	0.55
MISC54	0.63
MISC55	0.74
MISC56	0.66
MISC59	0.55
MISC60	0.60
MISC61	0.67
MISC62	0.52
MISC63	0.40
MISC64	0.60
MISC65	0.62
MISC66	0.70
MISC67	0.61
MISC68	0.22

2.7.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

	fanal17.communality	item
ATT41	0.30	ATT41
IMP49	0.39	IMP49
MISC68	0.22	MISC68

2.7.6.4 17 Factor Model Loadings

	PA9	PA1	PA2	PA4	PA3	PA5	PA7	PA8	PA6	PA13	PA10	PA17	PA12	PA11	PA14	PA16	PA15
TRAIN01	-0.02	0.18	-0.06	-0.05	-0.06	-0.08	-0.07	-0.03	0.08	-0.03	0.42	0.07	0.02	0.14	0.02	-0.08	0.36
TRAIN02	-0.02	0.01	0.03	0.03	0.08	0.05	0.04	0.02	-0.09	0.06	0.65	0.00	0.05	-0.02	-0.03	0.01	-0.07
TRAIN03	-0.01	-0.04	-0.03	-0.05	0.01	0.05	0.04	0.06	0.08	-0.09	0.73	0.05	0.05	0.03	0.03	0.02	-0.07
TRAIN04	0.06	0.31	-0.04	0.06	-0.04	-0.03	0.01	0.03	-0.06	0.03	0.49	0.15	-0.06	-0.03	-0.02	-0.15	0.10
TRAIN07	0.05	0.61	-0.09	0.04	-0.10	-0.06	-0.03	0.04	-0.01	0.02	0.26	0.00	0.00	-0.03	-0.03	0.02	0.04
TRAIN08	-0.01	0.07	-0.69	0.05	-0.04	0.08	0.04	0.01	-0.11	0.07	0.11	-0.07	0.01	0.05	0.00	0.05	0.06
AGG09	0.23	0.05	0.00	0.08	0.67	0.07	-0.08	-0.08	0.06	-0.03	0.00	0.09	0.01	-0.07	0.07	0.09	0.08
AGG10	-0.06	-0.03	0.08	0.10	0.79	-0.02	-0.02	0.12	0.05	0.03	0.02	0.00	0.02	0.00	-0.07	0.05	-0.03
AGG11	0.05	-0.12	-0.06	0.76	-0.09	0.01	-0.12	0.06	0.16	0.00	0.07	-0.04	0.06	0.08	0.10	0.04	0.24
AGG12	0.03	0.04	-0.07	0.88	0.05	0.02	0.06	0.04	0.02	0.01	-0.03	0.04	-0.05	-0.02	-0.06	-0.05	-0.19
AGG13	0.00	0.05	0.01	0.94	0.08	0.00	0.04	-0.06	-0.01	0.01	-0.01	0.04	0.07	0.02	0.00	-0.01	0.03
AGG14	0.06	0.07	0.04	-0.05	0.62	-0.01	0.05	0.12	0.10	-0.01	-0.03	0.01	-0.05	0.15	-0.14	0.04	-0.01
AGG15	0.29	-0.01	-0.05	0.08	0.72	0.02	-0.01	-0.04	0.10	-0.09	0.01	-0.04	0.09	0.03	0.08	-0.10	0.04
AGG16	-0.09	0.04	-0.06	-0.02	0.27	0.06	-0.03	-0.07	0.60	0.28	0.08	0.04	-0.05	-0.11	-0.02	0.09	-0.03
AGG17	0.05	0.12	0.15	0.15	0.28	0.09	0.18	0.15	0.03	0.01	-0.08	-0.08	0.17	-0.21	-0.29	-0.03	0.44
AGG18	-0.12	0.01	-0.01	-0.03	0.26	0.01	-0.07	-0.04	0.62	0.24	0.02	0.10	0.00	-0.08	0.02	0.09	0.03
AGG19	0.04	0.02	0.08	0.12	0.01	0.00	0.12	0.03	0.77	0.00	0.00	-0.09	0.08	-0.01	0.03	-0.08	0.04
AGG20	0.00	-0.05	0.03	0.31	-0.13	0.00	-0.01	0.05	0.58	-0.07	-0.03	0.09	0.09	0.07	-0.15	0.01	-0.03
FEAR21	0.81	-0.03	-0.02	0.04	0.08	0.01	-0.01	0.00	-0.01	0.08	-0.01	0.02	0.08	-0.03	0.02	0.05	0.05
FEAR22	0.38	0.17	0.03	-0.05	-0.21	0.20	0.06	0.05	0.20	-0.09	0.06	-0.08	0.06	0.13	-0.15	0.00	-0.18
FEAR23	0.75	0.01	-0.02	0.01	0.18	0.04	0.00	0.06	-0.02	0.16	-0.02	0.02	-0.04	-0.05	0.01	-0.01	-0.03
FEAR24	0.79	-0.02	-0.09	0.07	0.12	-0.03	0.03	-0.02	-0.04	0.17	0.00	-0.02	0.03	-0.03	0.02	0.08	0.01
FEAR25	0.39	0.26	0.13	0.10	-0.14	0.28	0.02	0.04	0.08	0.04	0.05	0.01	-0.06	0.11	-0.13	0.02	-0.01
FEAR26	0.31	-0.05	0.03	0.07	0.01	-0.03	-0.02	0.03	-0.01	0.11	0.06	0.02	0.42	-0.01	0.03	0.06	0.03
FEAR27	0.16	0.00	0.02	0.03	-0.03	0.02	0.00	0.04	0.06	0.85	-0.02	0.00	0.02	0.03	-0.01	-0.02	0.00
FEAR28	0.48	0.12	0.04	0.00	-0.09	0.33	0.06	0.02	-0.01	0.03	0.03	0.03	0.19	-0.09	-0.09	0.01	-0.06
FEAR29	-0.06	-0.03	-0.04	-0.01	0.02	-0.03	0.00	-0.01	-0.04	0.05	0.05	0.00	0.73	0.03	0.04	0.04	0.07
FEAR30	-0.03	0.03	0.01	0.01	-0.01	0.05	-0.01	0.06	0.05	0.01	-0.01	0.02	0.77	0.06	-0.02	-0.07	-0.09
FEAR31	0.11	0.02	-0.02	-0.03	-0.12	0.06	0.01	0.03	0.02	0.73	0.00	0.05	0.10	0.04	-0.06	0.01	0.00
SEPR32	0.08	-0.01	-0.07	-0.05	0.02	-0.05	0.08	0.75	0.06	-0.01	-0.03	0.06	0.08	-0.09	0.00	0.07	-0.05
SEPR33	-0.08	0.03	0.01	0.09	0.02	0.00	-0.01	0.78	-0.05	0.06	0.10	-0.02	0.03	0.01	0.04	0.04	-0.14
SEPR34	-0.02	0.01	0.00	-0.04	0.03	0.07	-0.02	0.80	-0.03	0.02	0.00	0.02	0.00	0.07	0.03	-0.03	0.19
EXCITE35	0.10	0.01	-0.11	-0.09	0.02	-0.08	0.61	0.14	0.04	0.01	0.07	-0.04	-0.03	0.04	0.12	0.10	-0.05
EXCITE36	-0.02	0.03	0.13	0.03	0.01	0.02	0.69	-0.05	-0.04	-0.06	0.00	0.04	0.05	-0.07	0.09	0.05	0.00
EXCITE37	-0.03	-0.02	-0.09	0.02	0.00	-0.03	0.78	0.01	0.02	0.03	0.01	0.04	-0.02	0.01	0.02	0.02	0.03
EXCITE38	-0.01	-0.09	0.04	0.03	-0.06	0.05	0.77	-0.03	0.03	0.01	0.01	0.05	-0.01	0.05	-0.03	-0.01	0.02
ATT39	0.02	-0.01	0.05	-0.03	0.00	-0.02	0.06	0.01	0.00	-0.03	0.00	-0.06	-0.02	0.04	0.05	0.82	0.01
ATT40	0.03	0.23	-0.16	-0.02	-0.04	0.06	0.02	0.07	0.00	-0.03	-0.10	0.21	0.06	-0.01	-0.15	0.42	0.07
ATT41	0.02	0.09	0.08	0.09	-0.12	0.00	0.01	0.10	0.06	-0.04	0.00	0.11	-0.04	0.21	0.05	0.37	-0.09
PLAY43	-0.29	0.05	0.53	0.01	-0.20	0.02	0.09	-0.02	-0.09	0.11	-0.03	-0.05	-0.03	0.08	0.12	-0.08	-0.13
PLAY44	-0.02	0.01	0.83	-0.01	-0.05	-0.03	0.03	-0.03	0.08	0.01	0.02	0.07	0.04	-0.10	0.05	0.04	0.01
PLAY45	0.01	0.00	0.84	-0.06	0.05	-0.04	-0.01	-0.04	-0.06	0.06	-0.04	0.02	0.00	0.01	0.06	0.06	-0.02
PLAY46	0.01	-0.11	0.80	0.00	0.07	0.01	0.02	0.05	-0.01	-0.07	0.04	0.00	-0.07	0.00	-0.01	-0.02	0.09
IMP47	0.03	-0.07	0.13	-0.05	0.01	0.00	0.09	-0.01	-0.01	0.04	0.11	0.67	0.01	0.08	0.02	-0.03	0.09
IMP48	-0.07	-0.01	0.05	0.14	0.03	0.01	0.08	0.05	-0.03	0.04	0.05	0.67	0.03	0.02	-0.01	-0.01	-0.12
IMP49	0.00	0.09	0.03	0.18	-0.02	-0.05	0.11	-0.08	-0.05	0.06	0.21	0.35	0.05	0.07	-0.04	-0.02	0.13
MISC51	0.02	0.10	-0.11	-0.07	-0.03	0.00	0.05	0.23	0.15	-0.07	0.00	0.19	-0.11	0.27	0.08	-0.12	0.38
MISC52	-0.03	0.03	-0.05	0.00	0.14	0.03	0.04	-0.05	-0.07	0.08	0.00	0.00	0.09	0.71	-0.05	0.10	-0.01
MISC53	-0.05	-0.04	-0.04	0.12	0.03	-0.04	-0.01	0.05	-0.03	0.01	0.05	0.10	0.06	0.65	0.01	-0.02	0.01
MISC54	0.01	0.12	-0.05	-0.06	-0.03	0.66	0.04	-0.04	0.01	0.00	0.02	0.04	0.13	0.06	-0.11	0.05	0.03
MISC55	0.01	-0.06	0.02	-0.05	0.03	0.87	0.00	0.06	0.05	0.01	0.04	-0.06	-0.02	-0.01	0.01	-0.04	-0.06
MISC56	-0.08	-0.03	-0.10	0.11	0.02	0.80	-0.04	-0.04	-0.06	0.05	-0.02	0.06	0.01	-0.02	0.10	0.00	0.09
MISC59	0.08	0.10	0.06	-0.02	-0.07	0.01	0.00	0.30	0.07	-0.10	-0.07	0.42	0.08	0.00	0.28	-0.02	-0.01
MISC60	0.00	0.05	0.12	0.02	-0.03	0.08	0.10	0.04	-0.08	-0.01	0.03	0.04	0.02	0.00	0.67	0.07	-0.01
MISC61	0.08	0.01	0.20	0.00	0.02	-0.03	0.15	0.14	0.05	-0.13	-0.02	0.03	-0.03	-0.06	0.61	0.05	0.00
MISC62	-0.08	0.46	-0.07	-0.06	0.08	-0.01	0.05	-0.05	0.25	0.26	-0.02	0.05	0.04	0.06	0.23	-0.02	-0.02
MISC63	0.00	0.47	-0.01	0.02	0.08	0.06	0.17	-0.08	0.04	0.08	-0.06	0.06	0.02	0.19	0.17	-0.09	-0.06
MISC64	-0.13	0.74	-0.03	0.07	0.04	0.01	-0.05	0.06	-0.06	0.02	0.04	-0.07	0.03	-0.01	0.01	0.06	0.10
MISC65	-0.08	0.67	-0.07	-0.05	0.03	-0.02	-0.04	0.04	0.07	0.05	0.08	0.05	0.06	0.06	0.01	0.01	0.06
MISC66	0.21	0.59	-0.08	-0.02	0.01	0.16	-0.07	0.06	-0.05	-0.03	0.05	0.11	0.06	0.00	-0.04	0.00	-0.09
MISC67	0.21	0.54	-0.13	0.01	-0.01	0.13	-0.06	0.05	0.03	-0.04	-0.01	0.09	0.05	0.00	-0.03	0.08	-0.13
MISC68	-0.08	0.09	0.08	0.25	0.01	0.20	0.06	0.12	-0.06	0.12	0.03	-0.01	-0.11	-0.03	0.07	-0.05	0.21

2.7.6.4.1 17 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
43	PA1	0.46	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
44	PA1	0.47	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
45	PA1	0.74	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
46	PA1	0.67	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
47	PA1	0.59	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
48	PA1	0.54	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
61	PA1	0.61	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
57	PA10	0.42	TRAIN01	Is hard to recall when off the leash
58	PA10	0.65	TRAIN02	Is slow to obey a ‘sit’ command
59	PA10	0.73	TRAIN03	Is slow to obey a ‘stay’ command
60	PA10	0.49	TRAIN04	Has difficulty attending/listening to things you say or do
62	PA10	0.11	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
35	PA11	0.71	MISC52	Begs persistently for food when people are eating
36	PA11	0.65	MISC53	Steals food
25	PA12	0.42	FEAR26	When examined/treated by a veterinarian
28	PA12	0.73	FEAR29	When having nails trimmed, or feet touched/handled
29	PA12	0.77	FEAR30	When groomed or bathed
26	PA13	0.85	FEAR27	When approached directly by an unfamiliar dog
30	PA13	0.73	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
41	PA14	0.67	MISC60	Playful, puppyish, boisterous
42	PA14	0.61	MISC61	Active, energetic, always on the go
9	PA15	0.44	AGG17	When stared at directly by you or another familiar person
34	PA15	0.38	MISC51	Escapes or would escape from home, yard or kennel given the chance
13	PA16	0.82	ATT39	Displays a strong attachment for you or another familiar person
14	PA16	0.42	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
15	PA16	0.37	ATT41	Tends to nudge or paw you (or others) for attention
31	PA17	0.67	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA17	0.67	IMP48	Becomes frustrated/impatient in a wide range of situations
33	PA17	0.35	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
40	PA17	0.42	MISC59	Hyperactive, restless, has trouble settling down
50	PA2	0.53	PLAY43	Eagerly engages in play with new/unfamiliar people
51	PA2	0.83	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
52	PA2	0.84	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
53	PA2	0.80	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.67	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.79	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.62	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.72	AGG15	When an unfamiliar person tries to touch or pet the dog
3	PA4	0.76	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.88	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.94	AGG13	When his/her food is taken away by you or another familiar person
49	PA4	0.25	MISC68	Chases own tail/hind end
37	PA5	0.66	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA5	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA5	0.80	MISC56	Nervous or frightened when ascending or descending some types of stairs
8	PA6	0.60	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA6	0.62	AGG18	When barked, growled, or lunged at by another dog
11	PA6	0.77	AGG19	Towards other familiar dogs
12	PA6	0.58	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
16	PA7	0.61	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17	PA7	0.69	EXCITE36	Excitable when playing with you or other familiar persons
18	PA7	0.78	EXCITE37	Excitable just before being taken out for a walk
19	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
54	PA8	0.75	SEPR32	Restlessness/agitation/pacing when left alone
55	PA8	0.78	SEPR33	Barking or whining when left alone
56	PA8	0.80	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
20	PA9	0.81	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21	PA9	0.38	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22	PA9	0.75	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23	PA9	0.79	FEAR24	When an unfamiliar person tries to touch or pet the dog
24	PA9	0.39	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27	PA9	0.48	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)

2.7.7 17 Model Reliability Measures

2.8 18 Factors

2.8.1 Imputation of Missing Items (18 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.8.2 18-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.8.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum18, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1639 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.8.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.8.3 18-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.8.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF18, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.8.3.2 18-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.8.4 Between-Item Correlations

2.8.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.892.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.893.

2.8.5 Estimating Number of Factors

2.8.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF18, n.obs = nrow(imputedNumericDF18), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 15.

2.8.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced

## In smc, smcs > 1 were set to 1.0

## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.

Number of Factors	MAP value
1	0.0272
2	0.0236
3	0.0184
4	0.0167
5	0.0159
6	0.0148
7	0.0144
8	0.0135
9	0.0135
10	0.0132
11	0.0128
12	0.0127
13	0.0130
14	0.0132
15	0.0136
16	0.0139
17	0.0143
18	0.0147

2.8.6 Factor Analysis for 18 Factors

2.8.6.1 18 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.

## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 5.1334475^{4}
  
• degrees of freedom: 928
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.1515229. Should be > 0.9; need reference)

2.8.6.2 18 Factor Model Communalities

	fanal18.communality
TRAIN01	0.59
TRAIN02	0.44
TRAIN03	0.62
TRAIN04	0.58
TRAIN07	0.62
TRAIN08	0.64
AGG09	0.81
AGG10	0.71
AGG11	0.82
AGG12	0.88
AGG13	1.00
AGG14	0.51
AGG15	0.83
AGG16	0.77
AGG17	0.77
AGG18	0.73
AGG19	0.75
AGG20	0.64
FEAR21	0.83
FEAR22	0.43
FEAR23	0.80
FEAR24	0.86
FEAR25	0.54
FEAR26	0.45
FEAR27	0.87
FEAR28	0.67
FEAR29	0.53
FEAR30	0.69
FEAR31	0.67
SEPR32	0.67
SEPR33	0.68
SEPR34	0.76
EXCITE35	0.51
EXCITE36	0.61
EXCITE37	0.60
EXCITE38	0.65
ATT39	0.67
ATT40	0.47
ATT41	0.31
PLAY43	0.59
PLAY44	0.81
PLAY45	0.78
PLAY46	0.74
IMP47	0.62
IMP48	0.61
IMP49	0.39
MISC51	0.52
MISC52	0.59
MISC53	0.54
MISC54	0.63
MISC55	0.74
MISC56	0.66
MISC59	0.56
MISC60	0.59
MISC61	0.68
MISC62	0.58
MISC63	0.57
MISC64	0.68
MISC65	0.64
MISC66	0.69
MISC67	0.61
MISC68	0.23

2.8.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

	fanal18.communality	item
ATT41	0.31	ATT41
IMP49	0.39	IMP49
MISC68	0.23	MISC68

2.8.6.4 18 Factor Model Loadings

	PA1	PA2	PA13	PA4	PA3	PA5	PA8	PA7	PA6	PA9	PA17	PA10	PA12	PA14	PA11	PA18	PA15	PA16
TRAIN01	-0.02	-0.05	0.12	-0.02	-0.07	-0.09	0.00	-0.07	0.03	-0.04	0.05	0.44	0.04	-0.02	0.10	0.12	-0.06	0.41
TRAIN02	-0.02	0.03	0.08	0.03	0.09	0.06	0.01	0.05	-0.09	0.06	0.01	0.62	0.05	-0.01	0.00	-0.10	-0.01	-0.08
TRAIN03	-0.02	-0.03	-0.05	-0.03	0.01	0.04	0.07	0.04	0.04	-0.09	0.04	0.75	0.05	0.02	0.02	0.01	0.03	-0.04
TRAIN04	0.06	-0.04	0.32	0.06	-0.04	-0.02	0.02	0.01	-0.06	0.03	0.17	0.47	-0.06	-0.02	-0.04	0.01	-0.15	0.09
TRAIN07	0.07	-0.09	0.60	0.02	-0.10	-0.05	0.02	-0.02	0.01	0.02	0.02	0.24	-0.01	-0.02	-0.03	0.06	0.01	0.01
TRAIN08	-0.01	-0.68	0.12	0.04	-0.04	0.09	0.00	0.05	-0.10	0.08	-0.07	0.09	0.01	0.01	0.06	-0.05	0.04	0.05
AGG09	0.22	0.01	-0.07	0.12	0.66	0.05	-0.04	-0.09	-0.01	-0.04	0.07	0.04	0.03	0.02	-0.12	0.20	0.12	0.12
AGG10	-0.06	0.08	0.00	0.09	0.79	-0.02	0.11	-0.02	0.04	0.04	0.00	0.01	0.01	-0.06	0.01	-0.03	0.05	-0.04
AGG11	0.04	-0.05	-0.09	0.76	-0.09	0.00	0.06	-0.12	0.15	0.00	-0.05	0.07	0.06	0.10	0.07	-0.05	0.04	0.25
AGG12	0.03	-0.07	0.00	0.89	0.04	0.02	0.05	0.06	0.02	0.01	0.04	-0.02	-0.04	-0.07	-0.03	0.06	-0.04	-0.19
AGG13	0.00	0.02	0.04	0.94	0.07	-0.01	-0.05	0.04	0.00	0.01	0.04	-0.01	0.07	0.00	0.02	0.01	-0.01	0.03
AGG14	0.07	0.04	0.09	-0.06	0.64	0.00	0.11	0.05	0.11	0.00	0.02	-0.04	-0.06	-0.13	0.16	-0.01	0.04	-0.02
AGG15	0.29	-0.06	0.04	0.06	0.73	0.03	-0.05	-0.01	0.11	-0.07	-0.02	-0.01	0.09	0.10	0.04	-0.03	-0.10	0.03
AGG16	-0.11	-0.05	-0.04	-0.01	0.27	0.06	-0.05	-0.04	0.52	0.29	0.02	0.11	-0.04	-0.04	-0.15	0.16	0.12	0.00
AGG17	0.05	0.16	0.18	0.15	0.29	0.09	0.14	0.20	0.04	0.02	-0.08	-0.10	0.17	-0.27	-0.20	-0.12	-0.04	0.39
AGG18	-0.14	-0.01	-0.06	-0.02	0.26	0.00	-0.02	-0.07	0.55	0.26	0.07	0.05	0.00	0.01	-0.11	0.14	0.12	0.06
AGG19	0.03	0.07	0.04	0.08	0.04	0.01	0.01	0.11	0.78	0.03	-0.07	0.00	0.07	0.05	-0.02	0.02	-0.08	0.04
AGG20	0.01	0.02	0.06	0.25	-0.10	0.02	0.00	-0.01	0.67	-0.04	0.13	-0.06	0.06	-0.10	0.10	-0.15	0.00	-0.06
FEAR21	0.81	-0.02	-0.01	0.04	0.08	0.01	-0.01	0.00	0.00	0.09	0.03	-0.01	0.08	0.03	-0.03	-0.03	0.04	0.05
FEAR22	0.38	0.03	0.10	-0.05	-0.21	0.19	0.06	0.05	0.21	-0.09	-0.09	0.07	0.06	-0.16	0.12	0.11	0.01	-0.16
FEAR23	0.75	-0.02	-0.02	0.02	0.17	0.04	0.06	-0.01	-0.03	0.16	0.01	-0.01	-0.04	0.00	-0.05	0.05	0.00	-0.03
FEAR24	0.79	-0.09	0.00	0.06	0.12	-0.03	-0.03	0.03	-0.03	0.17	-0.02	-0.01	0.03	0.03	-0.03	-0.04	0.07	0.00
FEAR25	0.40	0.14	0.11	0.13	-0.17	0.25	0.08	0.00	0.04	0.02	-0.02	0.08	-0.05	-0.18	0.08	0.23	0.05	0.03
FEAR26	0.32	0.03	0.03	0.05	0.02	-0.02	0.01	-0.01	0.02	0.12	0.03	0.04	0.41	0.06	0.02	-0.12	0.05	0.00
FEAR27	0.15	0.02	0.02	0.02	-0.03	0.03	0.03	0.00	0.05	0.86	0.01	-0.03	0.01	-0.01	0.03	0.01	-0.03	-0.01
FEAR28	0.48	0.05	0.04	0.01	-0.11	0.31	0.04	0.05	-0.02	0.02	0.01	0.05	0.20	-0.11	-0.10	0.10	0.03	-0.05
FEAR29	-0.06	-0.04	0.00	-0.01	0.02	-0.02	-0.01	0.01	-0.03	0.05	0.00	0.05	0.72	0.04	0.03	-0.04	0.04	0.06
FEAR30	-0.03	0.01	-0.02	0.02	-0.02	0.05	0.08	-0.02	0.04	0.00	0.02	0.01	0.78	-0.03	0.05	0.07	-0.06	-0.08
FEAR31	0.10	-0.02	0.02	-0.03	-0.12	0.06	0.03	0.01	0.00	0.73	0.05	0.00	0.10	-0.06	0.04	0.02	0.02	-0.01
SEPR32	0.07	-0.07	-0.02	-0.05	0.02	-0.06	0.75	0.08	0.06	-0.01	0.05	-0.03	0.09	0.01	-0.10	-0.01	0.07	-0.05
SEPR33	-0.07	0.01	0.03	0.10	0.02	0.00	0.79	-0.01	-0.05	0.05	-0.02	0.10	0.03	0.04	0.01	0.00	0.03	-0.15
SEPR34	-0.02	0.01	0.01	-0.03	0.03	0.06	0.82	-0.02	-0.03	0.02	0.02	0.00	0.00	0.02	0.05	0.00	-0.03	0.19
EXCITE35	0.10	-0.12	0.05	-0.10	0.03	-0.07	0.13	0.61	0.07	0.02	-0.02	0.06	-0.03	0.14	0.05	-0.04	0.09	-0.06
EXCITE36	-0.02	0.14	0.03	0.02	0.01	0.02	-0.06	0.68	-0.03	-0.06	0.05	-0.01	0.05	0.09	-0.06	0.00	0.05	-0.01
EXCITE37	-0.03	-0.09	-0.02	0.01	0.00	-0.02	0.01	0.77	0.03	0.03	0.05	0.01	-0.02	0.02	0.01	0.01	0.02	0.02
EXCITE38	-0.01	0.05	-0.14	0.05	-0.07	0.04	-0.01	0.76	0.02	0.00	0.04	0.02	0.00	-0.05	0.03	0.09	-0.01	0.04
ATT39	0.03	0.06	0.03	-0.04	0.01	-0.02	0.01	0.08	-0.01	-0.01	-0.08	-0.01	-0.03	0.09	0.06	-0.10	0.78	-0.02
ATT40	0.02	-0.14	0.10	0.01	-0.06	0.04	0.10	0.01	-0.07	-0.05	0.18	-0.08	0.08	-0.19	-0.06	0.17	0.48	0.11
ATT41	0.02	0.09	0.01	0.10	-0.13	-0.02	0.12	0.00	0.04	-0.04	0.08	0.03	-0.03	0.04	0.20	0.12	0.39	-0.07
PLAY43	-0.28	0.53	0.01	0.01	-0.21	0.01	-0.01	0.08	-0.09	0.09	-0.04	-0.02	-0.03	0.10	0.07	0.08	-0.08	-0.13
PLAY44	-0.02	0.83	0.01	-0.02	-0.05	-0.04	-0.03	0.04	0.07	0.01	0.07	0.02	0.04	0.06	-0.10	0.00	0.04	0.01
PLAY45	0.01	0.84	-0.01	-0.06	0.05	-0.04	-0.04	-0.01	-0.06	0.06	0.02	-0.04	0.00	0.07	0.01	0.01	0.05	-0.02
PLAY46	0.01	0.80	-0.08	0.00	0.08	0.01	0.04	0.03	0.00	-0.06	0.01	0.03	-0.07	0.01	0.01	-0.07	-0.03	0.08
IMP47	0.03	0.13	-0.03	-0.06	0.03	0.01	-0.02	0.10	0.01	0.05	0.67	0.09	0.01	0.03	0.08	-0.04	-0.03	0.09
IMP48	-0.07	0.05	0.01	0.13	0.04	0.02	0.04	0.08	-0.02	0.05	0.68	0.05	0.03	-0.01	0.03	0.00	0.00	-0.12
IMP49	0.00	0.03	0.12	0.17	-0.01	-0.05	-0.09	0.11	-0.04	0.06	0.35	0.20	0.05	-0.03	0.07	-0.02	-0.02	0.12
MISC51	0.01	-0.11	0.05	-0.06	-0.03	-0.01	0.25	0.04	0.13	-0.07	0.19	0.01	-0.10	0.06	0.23	0.12	-0.11	0.41
MISC52	-0.02	-0.05	0.03	-0.01	0.15	0.04	-0.05	0.04	-0.03	0.08	0.01	0.00	0.08	-0.04	0.72	0.03	0.10	0.00
MISC53	-0.06	-0.06	-0.05	0.12	0.03	-0.03	0.05	-0.01	-0.01	0.01	0.12	0.06	0.06	0.01	0.63	0.04	-0.01	0.03
MISC54	0.02	-0.05	0.09	-0.06	-0.03	0.65	-0.04	0.04	0.01	0.00	0.03	0.02	0.13	-0.12	0.06	0.04	0.06	0.03
MISC55	0.01	0.02	-0.04	-0.06	0.03	0.87	0.05	0.00	0.06	0.01	-0.05	0.04	-0.02	0.02	0.00	-0.02	-0.04	-0.07
MISC56	-0.08	-0.10	0.00	0.10	0.02	0.80	-0.04	-0.04	-0.06	0.05	0.07	-0.03	0.01	0.10	-0.01	-0.02	0.00	0.08
MISC59	0.08	0.05	0.10	-0.04	-0.07	0.02	0.28	-0.01	0.09	-0.10	0.44	-0.07	0.07	0.28	0.00	0.03	-0.02	-0.01
MISC60	0.01	0.12	0.03	0.01	-0.05	0.09	0.04	0.10	-0.08	-0.01	0.06	0.03	0.01	0.65	0.01	0.09	0.07	-0.01
MISC61	0.08	0.20	0.03	-0.01	0.02	-0.01	0.12	0.15	0.07	-0.12	0.05	-0.03	-0.05	0.62	-0.06	0.02	0.05	0.00
MISC62	-0.09	-0.06	0.21	-0.02	0.05	-0.05	0.00	0.02	0.15	0.24	0.01	0.03	0.06	0.16	-0.01	0.47	0.01	0.04
MISC63	-0.01	0.01	0.14	0.09	0.05	0.01	-0.01	0.14	-0.08	0.02	-0.01	-0.01	0.06	0.07	0.11	0.64	-0.06	0.01
MISC64	-0.11	-0.03	0.81	0.04	0.05	0.02	0.02	-0.04	-0.01	0.03	-0.05	-0.01	0.00	0.04	0.01	0.00	0.05	0.04
MISC65	-0.07	-0.07	0.65	-0.07	0.03	-0.01	0.02	-0.04	0.09	0.05	0.07	0.06	0.05	0.01	0.06	0.11	0.01	0.03
MISC66	0.23	-0.08	0.49	-0.03	0.00	0.16	0.06	-0.08	-0.05	-0.04	0.12	0.05	0.05	-0.06	-0.02	0.17	0.02	-0.09
MISC67	0.22	-0.14	0.47	-0.01	-0.02	0.13	0.04	-0.07	0.05	-0.04	0.10	-0.02	0.04	-0.03	-0.01	0.12	0.09	-0.14
MISC68	-0.08	0.08	0.17	0.23	0.02	0.21	0.10	0.06	-0.03	0.13	0.01	0.00	-0.12	0.09	-0.01	-0.09	-0.07	0.18

2.8.6.4.1 18 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
20	PA1	0.81	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21	PA1	0.38	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22	PA1	0.75	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23	PA1	0.79	FEAR24	When an unfamiliar person tries to touch or pet the dog
24	PA1	0.40	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27	PA1	0.48	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
57	PA10	0.44	TRAIN01	Is hard to recall when off the leash
58	PA10	0.62	TRAIN02	Is slow to obey a ‘sit’ command
59	PA10	0.75	TRAIN03	Is slow to obey a ‘stay’ command
60	PA10	0.47	TRAIN04	Has difficulty attending/listening to things you say or do
35	PA11	0.72	MISC52	Begs persistently for food when people are eating
36	PA11	0.63	MISC53	Steals food
25	PA12	0.41	FEAR26	When examined/treated by a veterinarian
28	PA12	0.72	FEAR29	When having nails trimmed, or feet touched/handled
29	PA12	0.78	FEAR30	When groomed or bathed
45	PA13	0.81	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
46	PA13	0.65	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
47	PA13	0.49	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
48	PA13	0.47	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
61	PA13	0.60	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
62	PA13	0.12	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
41	PA14	0.65	MISC60	Playful, puppyish, boisterous
42	PA14	0.62	MISC61	Active, energetic, always on the go
13	PA15	0.78	ATT39	Displays a strong attachment for you or another familiar person
14	PA15	0.48	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
15	PA15	0.39	ATT41	Tends to nudge or paw you (or others) for attention
9	PA16	0.39	AGG17	When stared at directly by you or another familiar person
34	PA16	0.41	MISC51	Escapes or would escape from home, yard or kennel given the chance
31	PA17	0.67	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA17	0.68	IMP48	Becomes frustrated/impatient in a wide range of situations
33	PA17	0.35	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
40	PA17	0.44	MISC59	Hyperactive, restless, has trouble settling down
43	PA18	0.47	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
44	PA18	0.64	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
50	PA2	0.53	PLAY43	Eagerly engages in play with new/unfamiliar people
51	PA2	0.83	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
52	PA2	0.84	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
53	PA2	0.80	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.66	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.79	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.64	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.73	AGG15	When an unfamiliar person tries to touch or pet the dog
3	PA4	0.76	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.89	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.94	AGG13	When his/her food is taken away by you or another familiar person
49	PA4	0.23	MISC68	Chases own tail/hind end
37	PA5	0.65	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA5	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA5	0.80	MISC56	Nervous or frightened when ascending or descending some types of stairs
8	PA6	0.52	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA6	0.55	AGG18	When barked, growled, or lunged at by another dog
11	PA6	0.78	AGG19	Towards other familiar dogs
12	PA6	0.67	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
16	PA7	0.61	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17	PA7	0.68	EXCITE36	Excitable when playing with you or other familiar persons
18	PA7	0.77	EXCITE37	Excitable just before being taken out for a walk
19	PA7	0.76	EXCITE38	Excitable just before being taken out for work or training
54	PA8	0.75	SEPR32	Restlessness/agitation/pacing when left alone
55	PA8	0.79	SEPR33	Barking or whining when left alone
56	PA8	0.82	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
26	PA9	0.86	FEAR27	When approached directly by an unfamiliar dog
30	PA9	0.73	FEAR31	When barked, growled, or lunged at by an unfamiliar dog

2.8.7 18 Model Reliability Measures